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Fraction Worksheets

Conversion :: Addition :: Subtraction :: Multiplication :: Division

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Fractions - addition, fractions - subtraction, fractions - multiplication, fractions - division.

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QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

  • The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
  • The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
  • The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
  • The calculus section will carry out differentiation as well as definite and indefinite integration.
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Online Fraction Calculator

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Fraction calculator

This is an online fraction calculator. This calculator not only gives you the answer but also the sample solution (i.e. steps) for your reference.

Fraction Calculator

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How to use this calculator

  • Fill in the blue boxes with numbers that are ranging 1 to 99. You can do this either by keying the numbers yourself or use the 'Generate Numbers' button.
  • Next, pick whether you want to add (+), subtract (-), multiply (×) or divide (÷) these fractions.
  • Click on the 'Calculate' button.

The sample answer and solution will be shown below the calculator.

  • Generate Numbers
  • Clear Boxes

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Sample Solution & Answer

The following are the sample solution and answer for your reference. Please be reminded that there might be a faster way of doing the calculation.

Ways to Use

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Using this calculator

You can use this calculator in many ways. Here are some ideas:

  • Check your fraction homework answers with it.
  • Use it to generate practice questions. Remember that practice makes perfect.
  • Use the sample solution as a guide to help you to solve questions that you are not sure about.

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Fractions Worksheets

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Adding and Subtracting Two Mixed Fractions with Similar Denominators, Mixed Fractions Results and Some Simplifying (Fillable)

Fraction Circles

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Fraction circle manipulatives are mainly used for comparing fractions, but they can be used for a variety of other purposes such as representing and identifying fractions, adding and subtracting fractions, and as probability spinners. There are a variety of options depending on your purpose. Fraction circles come in small and large versions, labeled and unlabeled versions and in three different color schemes: black and white, color, and light gray. The color scheme matches the fraction strips and use colors that are meant to show good contrast among themselves. Do note that there is a significant prevalence of color-blindness in the population, so don't rely on all students being able to differentiate the colors.

Suggested activity for comparing fractions: Photocopy the black and white version onto an overhead projection slide and another copy onto a piece of paper. Alternatively, you can use two pieces of paper and hold them up to the light for this activity. Use a pencil to represent the first fraction on the paper copy. Use a non-permanent overhead pen to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Adding fractions with fraction circles will involve two copies on paper. Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work.

  • Small Fraction Circles Small Fraction Circles in Black and White with Labels Small Fraction Circles in Color with Labels Small Fraction Circles in Light Gray with Labels Small Fraction Circles in Black and White Unlabeled Small Fraction Circles in Color Unlabeled Small Fraction Circles in Light Gray Unlabeled
  • Large Fraction Circles Large Fraction Circles in Black and White with Labels Large Fraction Circles in Color with Labels Large Fraction Circles in Light Gray with Labels Large Fraction Circles in Black and White Unlabeled Large Fraction Circles in Color Unlabeled Large Fraction Circles in Light Gray Unlabeled

Fraction Strips

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Fractions strips are often used for comparing fractions. Students are able to see quite easily the relationships and equivalence between fractions with different denominators. It can be quite useful for students to have two copies: one copy cut into strips and the other copy kept intact. They can then use the cut-out strips on the intact page to individually compare fractions. For example, they can use the halves strip to see what other fractions are equivalent to one-half. This can also be accomplished with a straight edge such as a ruler without cutting out any strips. Pairs or groups of strips can also be compared side-by-side if they are cut out. Addition and subtraction (etc.) are also possibilities; for example, adding a one-quarter and one-third can be accomplished by shifting the thirds strip so that it starts at the end of one-quarter then finding a strip that matches the end of the one-third mark (7/12 should do it).

Teachers might consider copying the fraction strips onto overhead projection acetates for whole class or group activities. Acetate versions are also useful as a hands-on manipulative for students in conjunction with an uncut page.

The "Smart" Fraction Strips include strips in a more useful order, eliminate the 7ths and 11ths strips as they don't have any equivalents and include 15ths and 16ths. The colors are consistent with the classic versions, so the two sets can be combined.

  • Classic Fraction Strips with Labels Classic Fraction Strips in Black and White With Labels Classic Fraction Strips in Color With Labels Classic Fraction Strips in Gray With Labels
  • Unlabeled Classic Fraction Strips Classic Fraction Strips in Black and White Unlabeled Classic Fraction Strips in Color Unlabeled Classic Fraction Strips in Gray Unlabeled
  • Smart Fraction Strips with Labels Smart Fraction Strips in Black and White With Labels Smart Fraction Strips in Color With Labels Smart Fraction Strips in Gray With Labels

Modeling fractions

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Fractions can represent parts of a group or parts of a whole. In these worksheets, fractions are modeled as parts of a group. Besides using the worksheets in this section, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?

  • Modeling Fractions with Groups of Shapes Coloring Groups of Shapes to Represent Fractions Identifying Fractions from Colored Groups of Shapes (Only Simplified Fractions up to Eighths) Identifying Fractions from Colored Groups of Shapes (Halves Only) Identifying Fractions from Colored Groups of Shapes (Halves and Thirds) Identifying Fractions from Colored Groups of Shapes (Halves, Thirds and Fourths) Identifying Fractions from Colored Groups of Shapes (Up to Fifths) Identifying Fractions from Colored Groups of Shapes (Up to Sixths) Identifying Fractions from Colored Groups of Shapes (Up to Eighths) Identifying Fractions from Colored Groups of Shapes (OLD Version; Print Too Light)
  • Modeling Fractions with Rectangles Modeling Halves Modeling Thirds Modeling Halves and Thirds Modeling Fourths (Color Version) Modeling Fourths (Grey Version) Coloring Fourths Models Modeling Fifths Coloring Fifths Models Modeling Sixths Coloring Sixths Models
  • Modeling Fractions with Circles Modeling Halves, Thirds and Fourths Coloring Halves, Thirds and Fourths Modeling Halves, Thirds, Fourths, and Fifths Coloring Halves, Thirds, Fourths, and Fifths Modeling Halves to Sixths Coloring Halves to Sixths Modeling Halves to Eighths Coloring Halves to Eighths Modeling Halves to Twelfths Coloring Halves to Twelfths

Ratio and Proportion Worksheets

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The equivalent fractions models worksheets include only the "baking fractions" in the A versions. To see more difficult and varied fractions, please choose the B to J versions after loading the A version. More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.

  • Picture Ratios Autumn Trees Part-to-Part Picture Ratios ( Grouped ) Autumn Trees Part-to-Part and Part-to-Whole Picture Ratios ( Grouped )
  • Equivalent Fractions Equivalent Fractions With Blanks ( Multiply Right ) ✎ Equivalent Fractions With Blanks ( Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply Right or Divide Left ) ✎ Equivalent Fractions With Blanks ( Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply Left ) ✎ Equivalent Fractions With Blanks ( Multiply Left or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide in Either Direction ) ✎ Are These Fractions Equivalent? (Multiplier 2 to 5) Are These Fractions Equivalent? (Multiplier 5 to 15) Equivalent Fractions Models Equivalent Fractions Models with the Simplified Fraction First Equivalent Fractions Models with the Simplified Fraction Second
  • Equivalent Ratios Equivalent Ratios with Blanks Only on Right Equivalent Ratios with Blanks Anywhere Equivalent Ratios with x 's

Comparing and Ordering Fractions

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Comparing fractions involves deciding which of two fractions is greater in value or if the two fractions are equal in value. There are generally four methods that can be used for comparing fractions. First is to use common denominators . If both fractions have the same denominator, comparing the fractions simply involves comparing the numerators. Equivalent fractions can be used to convert one or both fractions, so they have common denominators. A second method is to convert both fractions to a decimal and compare the decimal numbers. Visualization is the third method. Using something like fraction strips , two fractions can be compared with a visual tool. The fourth method is to use a cross-multiplication strategy where the numerator of the first fraction is multiplied by the denominator of the second fraction; then the numerator of the second fraction is multiplied by the denominator of the first fraction. The resulting products can be compared to decide which fraction is greater (or if they are equal).

  • Comparing Proper Fractions Comparing Proper Fractions to Sixths ✎ Comparing Proper Fractions to Ninths (No Sevenths) ✎ Comparing Proper Fractions to Ninths ✎ Comparing Proper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper Fractions to Twelfths ✎

The worksheets in this section also include improper fractions. This might make the task of comparing even easier for some questions that involve both a proper and an improper fraction. If students recognize one fraction is greater than one and the other fraction is less than one, the greater fraction will be obvious.

  • Comparing Proper and Improper Fractions Comparing Proper and Improper Fractions to Sixths ✎ Comparing Proper and Improper Fractions to Ninths (No Sevenths) ✎ Comparing Proper and Improper Fractions to Ninths ✎ Comparing Proper and Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper and Improper Fractions to Twelfths ✎ Comparing Improper Fractions to Sixths ✎ Comparing Improper Fractions to Ninths (No Sevenths) ✎ Comparing Improper Fractions to Ninths ✎ Comparing Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper Fractions to Twelfths ✎

This section additionally includes mixed fractions. When comparing mixed and improper fractions, it is useful to convert one of the fractions to the other's form either in writing or mentally. Converting to a mixed fraction is probably the better route since the first step is to compare the whole number portions, and if one is greater than the other, the proper fraction portion can be ignored. If the whole number portions are equal, the proper fractions must be compared to see which number is greater.

  • Comparing Proper, Improper and Mixed Fractions Comparing Proper, Improper and Mixed Fractions to Sixths ✎ Comparing Proper, Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Ninths ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths ✎
  • Comparing Improper and Mixed Fractions Comparing Improper and Mixed Fractions to Sixths ✎ Comparing Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Improper and Mixed Fractions to Ninths ✎ Comparing Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper and Mixed Fractions to Twelfths ✎
  • Comparing Mixed Fractions Comparing Mixed Fractions to Sixths ✎ Comparing Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Mixed Fractions to Ninths ✎ Comparing Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Mixed Fractions to Twelfths ✎

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.

  • Ordering Fractions with Easy Denominators on a Number Line Ordering Fractions with Easy Denominators to 10 on a Number Line Ordering Fractions with Easy Denominators to 24 on a Number Line Ordering Fractions with Easy Denominators to 60 on a Number Line Ordering Fractions with Easy Denominators to 100 on a Number Line
  • Ordering Fractions with Easy Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with Easy Denominators to 10 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 24 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 60 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 100 + Negatives on a Number Line
  • Ordering Fractions with All Denominators on a Number Line Ordering Fractions with All Denominators to 10 on a Number Line Ordering Fractions with All Denominators to 24 on a Number Line Ordering Fractions with All Denominators to 60 on a Number Line Ordering Fractions with All Denominators to 100 on a Number Line
  • Ordering Fractions with All Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with All Denominators to 10 + Negatives on a Number Line Ordering Fractions with All Denominators to 24 + Negatives on a Number Line Ordering Fractions with All Denominators to 60 + Negatives on a Number Line Ordering Fractions with All Denominators to 100 + Negatives on a Number Line

The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.

  • Ordering Positive Fractions Ordering Positive Fractions with Like Denominators Ordering Positive Fractions with Like Numerators Ordering Positive Fractions with Like Numerators or Denominators Ordering Positive Fractions with Proper Fractions Only Ordering Positive Fractions with Improper Fractions Ordering Positive Fractions with Mixed Fractions Ordering Positive Fractions with Improper and Mixed Fractions
  • Ordering Positive and Negative Fractions Ordering Positive and Negative Fractions with Like Denominators Ordering Positive and Negative Fractions with Like Numerators Ordering Positive and Negative Fractions with Like Numerators or Denominators Ordering Positive and Negative Fractions with Proper Fractions Only Ordering Positive and Negative Fractions with Improper Fractions Ordering Positive and Negative Fractions with Mixed Fractions Ordering Positive and Negative Fractions with Improper and Mixed Fractions

Simplifying & Converting Fractions Worksheets

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Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.

  • Rounding Fractions with Helper Lines Rounding Fractions to the Nearest Whole with Helper Lines Rounding Mixed Numbers to the Nearest Whole with Helper Lines Rounding Fractions to the Nearest Half with Helper Lines Rounding Mixed Numbers to the Nearest Half with Helper Lines
  • Rounding Fractions Rounding Fractions to the Nearest Whole Rounding Mixed Numbers to the Nearest Whole Rounding Fractions to the Nearest Half Rounding Mixed Numbers to the Nearest Half

Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

  • Simplifying Fractions Simplify Fractions (easier) Simplify Fractions (harder) Simplify Improper Fractions (easier) Simplify Improper Fractions (harder)
  • Converting Between Improper and Mixed Fractions Converting Mixed Fractions to Improper Fractions Converting Improper Fractions to Mixed Fractions Converting Between (both ways) Mixed and Improper Fractions
  • Converting Between Fractions and Decimals Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
  • Converting Between Fractions, Decimals, Percents and Ratios with Terminating Decimals Only Converting Fractions to Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Fractions to Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Part Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Part-to-Part Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Part-to-Whole Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only)
  • Converting Between Fractions, Decimals, Percents and Ratios with Terminating and Repeating Decimals Converting Fractions to Decimals, Percents and Part-to- Part Ratios Converting Fractions to Decimals, Percents and Part-to- Whole Ratios Converting Decimals to Fractions, Percents and Part-to- Part Ratios Converting Decimals to Fractions, Percents and Part-to- Whole Ratios Converting Percents to Fractions, Decimals and Part-to- Part Ratios Converting Percents to Fractions, Decimals and Part-to- Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios with 7ths and 11ths

Multiplying Fractions

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Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third OF a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Example: cut a loaf of bread in half, then cut the half into thirds. One third OF a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.

  • Multiplying Two Proper Fraction Multiplying Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ ✎ Multiplying Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with No Simplifying (Printable Only) Multiplying Two Proper Fractions with All Simplifying (Printable Only) Multiplying Two Proper Fractions with Some Simplifying (Printable Only)
  • Multiplying Proper and Improper Fractions Multiplying Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying Proper and Improper Fractions with Some Simplifying (Printable Only)
  • Multiplying Two Improper Fractions Multiplying Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with No Simplifying (Printable Only) Multiplying Two Improper Fractions with All Simplifying (Printable Only) Multiplying Two Improper Fractions with Some Simplifying (Printable Only)
  • Multiplying Proper and Mixed Fractions Multiplying Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying Two Mixed Fractions Multiplying Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with No Simplifying (Printable Only) Multiplying Two Mixed Fractions with All Simplifying (Printable Only) Multiplying Two Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying Whole Numbers and Proper Fractions Multiplying Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
  • Multiplying Whole Numbers and Improper Fractions Multiplying Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
  • Multiplying Whole Numbers and Mixed Fractions Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying Proper, Improper and Mixed Fractions Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying 3 Fractions Multiplying 3 Proper Fractions (Fillable, Savable, Printable) ✎ Multiplying 3 Proper and Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions and Whole Numbers (3 factors) (Fillable, Savable, Printable) ✎ Multiplying Fractions and Mixed Fractions (3 factors) (Fillable, Savable, Printable) ✎ Multiplying 3 Mixed Fractions (Fillable, Savable, Printable) ✎

Dividing Fractions

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Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?

  • Dividing Two Proper Fractions Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with No Simplifying (Printable Only) Dividing Two Proper Fractions with All Simplifying (Printable Only) Dividing Two Proper Fractions with Some Simplifying (Printable Only)
  • Dividing Proper and Improper Fractions Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
  • Dividing Two Improper Fractions Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with No Simplifying (Printable Only) Dividing Two Improper Fractions with All Simplifying (Printable Only) Dividing Two Improper Fractions with Some Simplifying (Printable Only)
  • Dividing Proper and Mixed Fractions Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
  • Dividing Two Mixed Fractions Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with No Simplifying (Printable Only) Dividing Two Mixed Fractions with All Simplifying (Printable Only) Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
  • Dividing Whole Numbers and Proper Fractions Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
  • Dividing Whole Numbers and Improper Fractions Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
  • Dividing Whole Numbers and Mixed Fractions Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
  • Dividing Proper, Improper and Mixed Fractions Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
  • Dividing 3 Fractions Dividing 3 Fractions Dividing 3 Fractions (Some Whole Numbers) Dividing 3 Fractions (Some Mixed) Dividing 3 Mixed Fractions

Multiplying and Dividing Fractions

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This section includes worksheets with both multiplication and division mixed on each worksheet. Students will have to pay attention to the signs.

  • Multiplying and Dividing Two Proper Fractions Multiplying and Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Proper and Improper Fractions Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Two Improper Fractions Multiplying and Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions (Printable Only)
  • Multiplying and Dividing Proper and Mixed Fractions Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Two Mixed Fractions Multiplying and Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Whole Numbers and Proper Fractions Fractions Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Whole Numbers and Improper Fractions Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Whole Numbers and Mixed Fractions Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing Proper, Improper and Mixed Fractions Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
  • Multiplying and Dividing 3 Fractions Multiplying/Dividing Fractions (three factors) Multiplying/Dividing Mixed Fractions (3 factors)

Adding Fractions

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Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?

  • Adding Two Proper Fractions with Equal Denominators and Proper Fraction Results Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
  • Adding Two Proper Fractions with Equal Denominators and Mixed Fraction Results Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
  • Adding Two Proper Fractions with Similar Denominators and Proper Fraction Results Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
  • Adding Two Proper Fractions with Similar Denominators and Mixed Fraction Results Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
  • Adding Two Proper Fractions with Unlike Denominators and Proper Fraction Results Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
  • Adding Two Proper Fractions with Unlike Denominators and Mixed Fraction Results Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
  • Adding Proper and Improper Fractions with Equal Denominators Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
  • Adding Proper and Improper Fractions with Similar Denominators Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
  • Adding Proper and Improper Fractions with Unlike Denominators Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)

A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.

  • Adding Two Mixed Fractions with Equal Denominators Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
  • Adding Two Mixed Fractions with Similar Denominators Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and Some Simplifying Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
  • Adding Two Mixed Fractions with Unlike Denominators Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)

Subtracting Fractions

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There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what it means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).

  • Subtracting Two Proper Fractions with Equal Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Two Proper Fractions with Similar Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Two Proper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Equal Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Similar Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Equal Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Similar Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Proper and Improper Fractions with Unlike Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
  • Subtracting Mixed Fractions with Equal Denominators Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Printable Only)
  • Subtracting Mixed Fractions with Similar Denominators Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Printable Only)
  • Subtracting Mixed Fractions with Unlike Denominators Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Printable Only)

Adding and Subtracting Fractions

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Mixing up the signs on operations with fractions worksheets makes students pay more attention to what they are doing and allows for a good test of their skills in more than one operation.

  • Adding and Subtracting Proper and Improper Fractions Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
  • Adding and Subtracting Mixed Fractions Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only) Adding/Subtracting Three Fractions/Mixed Fractions

All Operations Fractions Worksheets

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  • All Operations with Two Proper Fractions with Equal Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
  • All Operations with Two Proper Fractions with Similar Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
  • All Operations with Two Proper Fractions with Unlike Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Mixed Fractions Results and Some Simplifying (Printable Only)
  • All Operations with Proper and Improper Fractions with Equal Denominators All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
  • All Operations with Proper and Improper Fractions with Similar Denominators All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
  • All Operations with Proper and Improper Fractions with Unlike Denominators All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
  • All Operations with Two Mixed Fractions with Equal Denominators All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
  • All Operations with Two Mixed Fractions with Similar Denominators All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
  • All Operations with Two Mixed Fractions with Unlike Denominators All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)
  • All Operations with 3 Fractions All Operations with Three Fractions Including Some Improper Fractions All Operations with Three Fractions Including Some Negative and Some Improper Fractions

Operations with Negative Fractions Worksheets

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Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).

  • Adding with Negative Fractions Adding Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
  • Subtracting with Negative Fractions Subtracting Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Sixths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
  • Multiplying with Negative Fractions Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
  • Dividing with Negative Fractions Dividing Negative Proper Fractions with Denominators Up to Sixths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Twelfths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)

Order of Operations with Fractions Worksheets

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The order of operations worksheets in this section actually reside on the Order of Operations page, but they are included here for your convenience.

  • Order of Operations with Fractions 2-Step Order of Operations with Fractions 3-Step Order of Operations with Fractions 4-Step Order of Operations with Fractions 5-Step Order of Operations with Fractions 6-Step Order of Operations with Fractions
  • Order of Operations with Fractions (No Exponents) 2-Step Order of Operations with Fractions (No Exponents) 3-Step Order of Operations with Fractions (No Exponents) 4-Step Order of Operations with Fractions (No Exponents) 5-Step Order of Operations with Fractions (No Exponents) 6-Step Order of Operations with Fractions (No Exponents)
  • Order of Operations with Positive and Negative Fractions 2-Step Order of Operations with Positive & Negative Fractions 3-Step Order of Operations with Positive & Negative Fractions 4-Step Order of Operations with Positive & Negative Fractions 5-Step Order of Operations with Positive & Negative Fractions 6-Step Order of Operations with Positive & Negative Fractions

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Answered Problems By Math Tutors

A soccer coach wants to know how many hours a week his players spend training at home. He has 20 players and he decides to ask the first 4 players to arrive at Monday's soccer practice how many hours they spend training per week. He then calculated that they spend an average of 10 hour per week. Therefore, he assumed that all the players train 10 hours per week. Is this an example of a simple random sample? 

A No, because each student did not have an equal chance of being selected. 

B Yes, because each student had an equal chance of being selected. 

C No, because he did not sample every soccer player. 

D Yes, the minimum number of students sampled need to be four for it to be a simple random sample. 

The figure shows the graph of f. 

(b) Which of the cx-values A, B, C, D, E, F and G appear to be inflection points of f? 

The diagram shows two rectangles, A and B. 

All measurements are in centimetres. 

The area of rectangle A is equal to the area of rectangle B. 

Find an expression for y in terms of w. 

George's page contains twice as many typed words as Bill's page and Bill's page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on Bill's page and the number of words on Charlie's page is 210. How many words did Bill's page contain initially?

 Bill's page initially contained        words. 

Simplify 2sin(5x)cos(3x) - sin(2x) to one an expression containing one trigonometric function. Then graph the original function and your simplified version to verify they are identical. Enclose arguments of functions in parentheses. For example, sin(2x). 

2sin(5x)cos(3x)-sin(2x)=

A health psychologist was interested in the effects of vitamin supplements on the immune system. Three groups of adults were exposed (in a highly ethical way) to the cold virus; one group took no supplements for a week before exposure, another had vitamin C supplements, and a third had multivitamins (excluding C). The severity of the cold was measured as a percentage (0% = not contracted, 100% very severe symptoms). The psychologist also measured the number of cigarettes that each person smoked per day, as smoking suppresses the immune system. The psychologist was interested in the differences in the severity of the illnesses across different vitamin groups accounting for cigarette usage. What technique should be used to analyse these data? 

A. Two-way repeated-measures ANOVA 

B. Two-way independent ANOVA 

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Fractions Worksheets

Fraction worksheets for grades 1 through 6.

Our fraction worksheets start with the introduction of the concepts of " equal parts ", "parts of a whole" and "fractions of a group or set"; and proceed to operations on fractions and mixed numbers.  

Choose your grade / topic:

Grade 1 fraction worksheets, grade 2 fraction worksheets, grade 3 fraction worksheets.

Fraction worksheets

Fractions to decimals

Fraction addition and subtraction

Fraction multiplication and division

Converting fractions, equivalent fractions, simplifying fractions

Fraction to / from decimals 

Fraction addition and subtraction 

Fraction multiplication and division worksheets

Fraction to / from decimals

Topics include:

  • Identifying "equal parts"
  • Dividing shapes into "equal parts"
  • Parts of a whole
  • Fractions in words
  • Coloring shapes to make fractions
  • Writing fractions
  • Fractions of a group or set
  • Word problems: write the fraction from the story
  • Equal parts
  • Numerators and denominators of a fraction
  • Writing fractions from a numerator and denominator
  • Reading fractions and matching to their words
  • Writing fractions in words
  • Identifying common fractions (matching, coloring, etc)
  • Fractions as part of a set or group (identifying, writing, coloring, etc)
  • Using fractions to describe a set
  • Comparing fractions with pie charts (parts of whole, same denominator)
  • Comparing fractions with pie charts (same numerator, different denominators)
  • Comparing fractions with pictures (parts of sets)
  • Comparing fractions with block diagrams
  • Understanding fractions word problems
  • Writing and comparing fractions word problems
  • Identifying fractions
  • Fractional part of a set
  • Identifying equivalent fractions
  • Equivalent fractions - missing numerators, denominators
  • 3 Equivalent fractions
  • Comparing fractions with pie charts (same denominator)
  • Comparing proper fractions with pie charts
  • Comparing proper or improper fractions with pie charts
  • Compare mixed numbers with pie charts
  • Comparing fractions (like, unlike denominators)
  • Compare improper fractions, mixed numbers
  • Simplifying fractions (proper, improper)
  • Adding like fractions
  • Adding mixed numbers
  • Completing whole numbers
  • Subtracting like fractions
  • Subtracting a fraction from a whole number or mixed number
  • Subtracting mixed numbers
  • Converting fractions to / from mixed numbers
  • Converting mixed numbers and fractions to / from decimals
  • Fractions word problems

Grade 4 fraction worksheets

  • Adding like fractions (denominators 2-12)
  • Adding like fractions (all denominators)
  • Adding fractions and mixed numbers (like denominators)
  • Subtracting like fractions (denominators 2-12)
  • Subtracting fractions from whole numbers, mixed numbers
  • Subtracting mixed numbers from mixed numbers or whole numbers
  • Comparing improper fractions and mixed numbers with pie charts
  • Comparing proper and improper fractions
  • Ordering 3 fractions
  • Identifying equivalent fractions (pie charts)
  • Writing equivalent fractions (pie charts)
  • Equivalent fractions with missing numerators or denominators

Grade 4 fractions to decimals worksheets

  • Convert decimals to fractions (tenths, hundredths)
  • Convert decimals to mixed numbers (tenths, hundredths)
  • Convert fractions to decimals (denominator of 10 or 100)
  • Convert mixed numbers to decimals (denominator of 10 or 100)

Grade 5 addition and subtraction of fractions worksheets

  • Adding like fractions (denominators 2-25)
  • Adding mixed numbers and / or fractions (like denominators)
  • Adding unlike fractions & mixed numbers
  • Subtracting fractions from whole numbers and mixed numbers (same denominators)
  • Subtracting mixed numbers with missing subtrahend or minuend)
  • Subtracting unlike fractions
  • Subtracting mixed numbers (unlike denominators)
  • Word problems on adding and subtracting fractions

Grade 5 fraction multiplication and division worksheets

  • Multiply fractions by whole numbers
  • Multiply fractions by fractions
  • Multiply improper fractions
  • Multiply fractions by mixed numbers
  • Multiply mixed numbers by mixed numbers
  • Missing factor questions
  • Divide whole numbers by fractions (answers are whole numbers)
  • Divide a fraction by a whole number and vice versa
  • Divide mixed numbers by fractions
  • Divide fractions by fractions
  • Mixed numbers divided by mixed numbers
  • Word problems on multiplying and dividing fractions
  • Mixed operations with fractions word problems

Grade 5 converting, simplifying & equivalent fractions

  • Converting improper fractions to / from mixed numbers
  • Simplifying proper fractions
  • Simplifying proper and improper fractions
  • Equivalent fractions (2 fractions)
  • Equivalent fractions (3 fractions)

Grade 5 fraction to / from decimals worksheets

  • Convert decimals to fractions (tenths, hundredths), no simplification
  • Convert decimals to fractions (tenths, hundredths), with simplification
  • Convert decimals to mixed numbers
  • Convert fractions to decimals (denominators of 10 or 100)
  • Convert mixed numbers to decimals (denominators of 10 or 100)
  • Convert mixed numbers to decimals (denominators of 10, 100 or 1000)
  • Convert fractions to decimals (common denominators of 2, 4, 5, ...)
  • Convert mixed numbers to decimals (common denominators of 2, 4, 5, ...)
  • Convert fractions to decimals, some with repeating decimals

Grade 6 addition and subtraction of fractions worksheets

  • Adding unlike fractions
  • Adding  fractions and mixed numbers
  • Adding mixed numbers (unlike denominators)
  • Subtract unlike fractions
  • Subtract mixed numbers (unlike denominators)

Grade 6 fraction multiplication and division worksheets

  • Fractions multiplied by whole numbers
  • Fractions multiplied by fractions
  • Mixed numbers multiplied by fractions
  • Mixed numbers multiplied by mixed numbers
  • Whole numbers divided by fractions
  • Fractions divided by fractions
  • Mixed numbers divided by mixed nuymbers
  • Mixed multiplication or division practice

Grade 6 converting, simplifying and equivalent fractions worksheets

  • Convert improper fractions to / from mixed numbers
  • Simplify proper fractions
  • Simplify proper and improper fractions
  • Equivalent fractions (4 fractions)

Grade 6 fraction to / from decimals worksheets

  • Convert decimals to fractions, with simplification
  • Convert decimals to mixed numbers, with simplification
  • Convert fractions to decimals (denominators are 10 or 100)
  • Convert fractions to decimals (various denominators)
  • Convert mixed numbers to decimals (various denominators)

Related topics

Decimals worksheets

Word problem worksheets

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Sample Fractions Worksheet

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Mathematics LibreTexts

1.4: Fractions

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  • Page ID 18329

Learning Objectives

  • Reduce a fraction to lowest terms.
  • Multiply and divide fractions.
  • Add and subtract fractions.

A fraction is a real number written as a quotient, or ratio, of two integers \(a\) and \(b\), where \(b \neq 0\).

https://2012books.lardbucket.org/books/beginning-algebra/section_04/c1e301b3aeb14755a7739e70039397e5.jpg

The integer above the fraction bar is called the numerator and the integer below is called the denominator . The numerator is often called the “part” and the denominator is often called the “whole.” Equivalent fractions are two equal ratios expressed using different numerators and denominators. For example,

\(\frac{50}{100} = \frac{1}{2}\)

Fifty parts out of \(100\) is the same ratio as \(1\) part out of \(2\) and represents the same real number. Consider the following factorizations of \(50\) and \(100\):

\[ \begin{align*} 50 &= 2 \cdot 25 \\ 100 &= 4 \cdot 25 \end{align*} \]

The numbers \(50\) and \(100\) share the factor \(25\). A shared factor is called a common factor. We can rewrite the ratio \(\frac{50}{100}\) as follows:

\(\frac{50}{100} = \frac{2 \cdot 25}{4 \cdot 25}\)

Making use of the multiplicative identity property and the fact that \(\frac{25}{25} = 1\), we have

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Dividing \(\frac{25}{25}\) and replacing this factor with a \(1\) is called canceling . Together, these basic steps for finding equivalent fractions define the process of reducing . Since factors divide their product evenly, we achieve the same result by dividing both the numerator and denominator by \(25\) as follows:

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Finding equivalent fractions where the numerator and denominator have no common factor other than \(1\) is called reducing to lowest terms . When learning how to reduce to lowest terms, it is helpful to first rewrite the numerator and denominator as a product of primes and then cancel. For example,

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We achieve the same result by dividing the numerator and denominator by the greatest common factor (GCF). The GCF is the largest number that divides both the numerator and denominator evenly. One way to find the GCF of \(50\) and \(100\) is to list all the factors of each and identify the largest number that appears in both lists. Remember, each number is also a factor of itself.

\[ \begin{align*} &\{1,2,5,10,25,50\} && \color{Cerulean}{Factors\ of\ 50} \\ &\{1,2,4,5,10,20,25,50,100\} && \color{Cerulean}{Factors\ of\ 100} \end{align*} \]

Common factors are listed in bold, and we see that the greatest common factor is \(50\). We use the following notation to indicate the GCF of two numbers: GCF\((50, 100) = 50\). After determining the GCF, reduce by dividing both the numerator and the denominator as follows:

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Example \(\PageIndex{1}\)

Reduce to lowest terms: \(\frac{105}{300}\).

Rewrite the numerator and denominator as a product of primes and then cancel.

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Alternatively, we achieve the same result if we divide both the numerator and denominator by the GCF\((105, 300)\). A quick way to find the GCF of the two numbers requires us to first write each as a product of primes. The GCF is the product of all the common prime factors.

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In this case, the common prime factors are \(3\) and \(5\) and the greatest common factor of \(105\) and \(300\) is \(15\).

https://2012books.lardbucket.org/books/beginning-algebra/section_04/76d1cd06699f306be99ea2f093343579.jpg

\(\frac{7}{20}\)

Example \(\PageIndex{2}\)

Try this! Reduce to lowest terms: \(\frac{32}{96}\).

Video Solution:

(click to see video)

An improper fraction is one where the numerator is larger than the denominator. A mixed number is a number that represents the sum of a whole number and a fraction. For example, \(5 \frac{1}{2}\) is a mixed number that represents the sum \(5+\frac{1}{2}\). Use long division to convert an improper fraction to a mixed number; the remainder is the numerator of the fractional part.

Example \(\PageIndex{3}\)

Write \(\frac{23}{5}\) as a mixed number.

Notice that \(5\) divides into \(23\) four times with a remainder of \(3\).

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We then can write

\[ \begin{align*} \frac{23}{5} &= 4 + \frac{3}{5} \\ &= 4 \frac{3}{5} \end{align*} \]

Note that the denominator of the fractional part of the mixed number remains the same as the denominator of the original fraction.

\(4 \frac{3}{5}\)

To convert mixed numbers to improper fractions, multiply the whole number by the denominator and then add the numerator; write this result over the original denominator.

Example \(\PageIndex{4}\)

Write \(3 \frac{5}{7}\) as an improper fraction.

Obtain the numerator by multiplying \(7\) times \(3\) and then add \(5\).

\[ \begin{align*} 3 \frac{5}{7} &= \frac{7 \cdot 3 + 5}{7} \\ &= \frac{21+5}{7} \\ &= \frac{26}{7} \end{align*} \]

\(\frac{26}{7}\)

It is important to note that converting to a mixed number is not part of the reducing process. We consider improper fractions, such as \(267\), to be reduced to lowest terms. In algebra it is often preferable to work with improper fractions, although in some applications, mixed numbers are more appropriate.

Example \(\PageIndex{5}\)

Try this! Convert \(10 \frac{1}{2}\) to an improper fraction.

Multiplying and Dividing Fractions

In this section, assume that \(a, b, c\), and \(d\) are all nonzero integers. The product of two fractions is the fraction formed by the product of the numerators and the product of the denominators. In other words, to multiply fractions, multiply the numerators and multiply the denominators:

\(\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}\)

Example \(\PageIndex{6}\)

Multiply: \(\frac{2}{3} \cdot \frac{5}{7}\)

Multiply the numerators and multiply the denominators.

\[ \begin{align*} \frac{2}{3} \cdot \frac{5}{7} &= \frac{2 \cdot 5}{3 \cdot 7} \\ &= \frac{10}{21} \end{align*} \]

\(\frac{10}{21}\)

Example \(\PageIndex{7}\)

Multiply: \(\frac{5}{9}\left(-\frac{1}{4}\right)\)

Recall that the product of a positive number and a negative number is negative.

\[ \begin{align*} \frac{5}{9}\left(-\frac{1}{4}\right) &= -\frac{5 \cdot 1}{9 \cdot 4} \\ &= -\frac{5}{36} \end{align*} \]

\(-\frac{5}{36}\)

Example \(\PageIndex{8}\)

Multiply: \(\frac{2}{3} \cdot 5 \frac{3}{4}\)

Begin by converting \(5 \frac{3}{4}\) to an improper fraction.

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In this example, we noticed that we could reduce before we multiplied the numerators and the denominators. Reducing in this way is called cross canceling , and can save time when multiplying fractions.

\(3 \frac{5}{6}\)

Two real numbers whose product is \(1\) are called reciprocals . Therefore, \(\frac{a}{b}\) and \(\frac{b}{a}\) are reciprocals because \( \frac{a}{b} \cdot \frac{b}{a} = \frac{ab}{ab} = 1\). For example,

\(\frac{2}{3} \cdot \frac{3}{2} = \frac{6}{6} = 1\)

Because their product is \(1\), \(\frac{2}{3}\) and \(\frac{3}{2}\) are reciprocals. Some other reciprocals are listed below:

\(\frac{5}{8}\ \text{and}\ \frac{8}{5} \qquad 7\ \text{and}\ \frac{1}{7} \qquad -\frac{4}{5}\ \text{and}\ -\frac{5}{4}\)

This definition is important because dividing fractions requires that you multiply the dividend by the reciprocal of the divisor.

\(\frac{a}{b} \div \color{Cerulean}{\frac{c}{d}} \color{Black}{=} \frac{a}{b} \cdot \color{Cerulean}{\frac{d}{c}} \color{Black}{=} \frac{ad}{bc} \)

Example \(\PageIndex{9}\)

Divide: \(\frac{2}{3} \div \frac{5}{7}\)

Multiply \(\frac{2}{3}\) by the reciprocal of \(\frac{5}{7}\).

\[ \begin{align*} \frac{2}{3} \div \frac{5}{7} &= \frac{2}{3} \cdot \frac{7}{5} \\ &= \frac{2 \cdot 7}{3 \cdot 5 } \\ &= \frac{14}{15} \end{align*} \]

\(\frac{14}{15\)

You also need to be aware of other forms of notation that indicate division: / and —. For example,

\(5/(1/2) = 5*(2/1)=(5/1)*(2/1)= 10/1=10\)

\(\frac{\frac{7}{8}}{\color{Cerulean}{\frac{2}{3}}} \color{Black}{=} \frac{7}{8} \div \color{Cerulean}{\frac{2}{3}} \color{Black}{=} \frac{7}{8} \cdot \color{Cerulean}{\frac{3}{2}} \color{Black}{=} \frac{21}{16}\)

The latter is an example of a complex fraction , which is a fraction whose numerator, denominator, or both are fractions.

Students often ask why dividing is equivalent to multiplying by the reciprocal of the divisor. A mathematical explanation comes from the fact that the product of reciprocals is \(1\). If we apply the multiplicative identity property and multiply numerator and denominator by the reciprocal of the denominator, then we obtain the following:

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Before multiplying, look for common factors to cancel; this eliminates the need to reduce the end result.

Example \(\PageIndex{10}\)

Divide: \(\frac{\frac{5}{2}}{\frac{7}{4}}\).

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\(\frac{10}{7}\)

When dividing by an integer, it is helpful to rewrite it as a fraction over \(1\).

Example \(\PageIndex{11}\)

Divide: \(\frac{2}{3} \div 6\)

Rewrite 6 as \(\frac{6}{1}\) and multiply by its reciprocal.

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\(\frac{1}{9}\)

Also, note that we only cancel when working with multiplication. Rewrite any division problem as a product before canceling.

Example \(\PageIndex{12}\)

Try this! Divide: \(5 \div 2 \frac{3}{5} \)

Adding and Subtracting Fractions

Negative fractions are indicated with the negative sign in front of the fraction bar, in the numerator, or in the denominator. All such forms are equivalent and interchangeable.

\(\frac{-3}{4} = -\frac{3}{4} = \frac{3}{-4}\)

Adding or subtracting fractions requires a common denominator . In this section, assume the common denominator c is a nonzero integer.

It is good practice to use positive common denominators by expressing negative fractions with negative numerators. In short, avoid negative denominators.

Example \(\PageIndex{13}\)

Subtract: \(\frac{12}{15} - \frac{3}{15}\)

The two fractions have a common denominator \(15\). Therefore, subtract the numerators and write the result over the common denominator:

\[ \begin{align*} \frac{12}{15} - \frac{3}{15} &= \frac{12-3}{15} && \color{Cerulean}{Subtract\ the\ numerators.} \\ &= \color{Black}{\frac{9}{15}} \\ &=\frac{9 \color{Cerulean}{\div 3}}{\color{Black}{15} \color{Cerulean}{\div 3}} &&\color{Cerulean}{Reduce.} \\ &= \frac{3}{5} \end{align*} \]

Answer \(\frac{3}{5}\)

Most problems that you are likely to encounter will have unlike denominators . In this case, first find equivalent fractions with a common denominator before adding or subtracting the numerators. One way to obtain equivalent fractions is to divide the numerator and the denominator by the same number. We now review a technique for finding equivalent fractions by multiplying the numerator and the denominator by the same number. It should be clear that \(5/5\) is equal to \(1\) and that \(1\) multiplied times any number is that number:

\(\frac{1}{2} = \frac{1}{2} \cdot \color{Cerulean}{1} \color{Black}{=} \frac{1}{2} \cdot \color{Cerulean}{\frac{5}{5}} \color{Black}{=} \frac{5}{10}\)

We have equivalent fractions \(\frac{1}{2}=\frac{5}{10}\). Use this idea to find equivalent fractions with a common denominator to add or subtract fractions. The steps are outlined in the following example.

Example \(\PageIndex{14}\)

Subtract: \(\frac{7}{15} - \frac{3}{10}\)

Step 1: Determine a common denominator. To do this, use the least common multiple (LCM) of the given denominators. The LCM of \(15\) and \(10\) is indicated by LCM\((15, 10)\). Try to think of the smallest number that both denominators divide into evenly. List the multiples of each number:

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Common multiples are listed in bold, and the least common multiple is \(30\).

LCM\((10,15)=30\)

Step 2: Multiply the numerator and the denominator of each fraction by values that result in equivalent fractions with the determined common denominator.

\[\begin{align*} \frac{7}{15} - \frac{3}{10} &= \frac{7 \color{Cerulean}{\cdot 2}}{15 \color{Cerulean}{\cdot 3}} - \frac{3\color{Cerulean}{\cdot 3}}{10 \color{Cerulean}{\cdot 3}} \\ &= \frac{14}{30} - \frac{9}{30} \end{align*}\]

Step 3: Add or subtract the numerators, write the result over the common denominator and then reduce if possible.

\[\begin{align*} \frac{14}{30} - \frac{9}{30} &= \frac{14-9}{30} \\ &= \frac{5}{30} \\ &= \frac{5 \color{Cerulean}{\div 5}}{30 \color{Cerulean}{\div 5}} \\ &= \frac{1}{6} \end{align*}\]

\(\frac{1}{6}\)

The least common multiple of the denominators is called the least common denominator (LCD). Finding the LCD is often the difficult step. It is worth finding because if any common multiple other than the least is used, then there will be more steps involved when reducing.

Example \(\PageIndex{15}\)

Add: \(\frac{5}{10} + \frac{1}{18}\)

First, determine that the LCM\((10, 18)\) is \(90\) and then find equivalent fractions with \(90\) as the denominator.

\[\begin{align*} \frac{5}{10} + \frac{1}{18} &= \frac{5 \color{Cerulean}{\cdot 9}}{10 \color{Cerulean}{\cdot 9}} + \frac{1 \color{Cerulean}{\cdot 5}}{18 \color{Cerulean}{\cdot 5}} \\ &= \frac{45}{90} + \frac{5}{90} \\ &= \frac{45+5}{90} \\ &= \frac{50}{90} \\ &= \frac{50 \color{Cerulean}{\div 10}}{90 \color{Cerulean}{\div 10}} \\ &= \frac{5}{9} \end{align*}\]

\(\frac{5}{9}\)

Example \(\PageIndex{16}\)

Try this! Add: \(\frac{2}{30} + \frac{5}{21}\)

Example \(\PageIndex{17}\)

Simplify: \(2 \frac{1}{3} + \frac{3}{5} - \frac{1}{2}\)

Begin by converting \(2 \frac{1}{3}\) to an improper fraction.

clipboard_e7e9738610c56f1a7c329f3819ae3778f.png

\(2 \frac{13}{30}\)

In general, it is preferable to work with improper fractions. However, when the original problem involves mixed numbers, if appropriate, present your answers as mixed numbers. Also, mixed numbers are often preferred when working with numbers on a number line and with real-world applications.

Example \(\PageIndex{18}\)

Try this! Subtract: \(\frac{5}{7} - 2 \frac{1}{7}\)

Example \(\PageIndex{19}\)

How many \(\frac{1}{2}\) inch thick paperback books can be stacked to fit on a shelf that is \(1 \frac{1}{2}\) feet in height?

First, determine the height of the shelf in inches. To do this, use the fact that there are \(12\) inches in \(1\) foot and multiply as follows:

clipboard_ed64be26f369e37959027b418e41aa38b.png

Next, determine how many notebooks will fit by dividing the height of the shelf by the thickness of each book.

clipboard_e628fb6f31ac27f7376e007050de71417.png

\(36\) books can be stacked on the shelf.

Key Takeaways:

  • Fractions are not unique; there are many ways to express the same ratio. Find equivalent fractions by multiplying or dividing the numerator and the denominator by the same real number.
  • Equivalent fractions in lowest terms are generally preferred. It is a good practice to always reduce.
  • In algebra, improper fractions are generally preferred. However, in real-life applications, mixed number equivalents are often preferred. We may present answers as improper fractions unless the original question contains mixed numbers, or it is an answer to a real-world or geometric application.
  • Multiplying fractions does not require a common denominator; multiply the numerators and multiply the denominators to obtain the product. It is a best practice to cancel any common factors in the numerator and the denominator before multiplying.
  • Reciprocals are rational numbers whose product is equal to \(1\). Given a fraction \(\frac{a}{b}\), its reciprocal is \(\frac{b}{a}\).
  • Divide fractions by multiplying the dividend by the reciprocal of the divisor. In other words, multiply the numerator by the reciprocal of the denominator.
  • Rewrite any division problem as a product before canceling.
  • Adding or subtracting fractions requires a common denominator. When the denominators of any number of fractions are the same, simply add or subtract the numerators and write the result over the common denominator.
  • Before adding or subtracting fractions, ensure that the denominators are the same by finding equivalent fractions with a common denominator. Multiply the numerator and the denominator of each fraction by the appropriate value to find the equivalent fractions.
  • Typically, it is best to convert all mixed numbers to improper fractions before beginning the process of adding, subtracting, multiplying, or dividing.

Exercise \(\PageIndex{1}\)

Reduce each fraction to lowest terms.

1. \(\frac{5}{30}\)

2. \(\frac{6}{24}\)

3. \(\frac{30}{70}\)

4. \(\frac{18}{27}\)

5. \(\frac{44}{84}\)

6. \(\frac{54}{90}\)

7. \(\frac{135}{30}\)

8. \(\frac{105}{300}\)

9. \(\frac{18}{6}\)

10. \(\frac{256}{16}\)

11. \(\frac{126}{45}\)

12. \(\frac{52}{234}\)

13. \(\frac{54}{162}\)

14. \(\frac{2000}{3000}\)

15. \(\frac{270}{360}\)

5: \(11/21\)

11: \(14/5\)

13: \(1/3\)

15: \(3/4\)

Exercise \(\PageIndex{2}\)

Rewrite as an improper fraction.

  • \(4\frac{3}{4}\)
  • \(2\frac{1}{2}\)
  • \(5\frac{7}{15}\)
  • \(1\frac{1}{2}\)
  • \(3\frac{5}{8}\)
  • \(1\frac{3}{4}\)
  • \(−2\frac{1}{2}\)
  • \(−1\frac{3}{4}\)

7: \(−7/4\)

Exercise \(\PageIndex{3}\)

Rewrite as a mixed number.

  • \(\frac{15}{2}\)
  • \(\frac{9}{2}\)
  • \(\frac{40}{13}\)
  • \(\frac{103}{25}\)
  • \(\frac{73}{10}\)
  • \(\frac{−52}{7}\)
  • \(\frac{−59}{6}\)

2: \(4\frac{1}{2}\)

4: \(4\frac{3}{25}\)

6: \(−7\frac{3}{7}\)

Exercise \(\PageIndex{4}\)

Multiply and reduce to lowest terms.

  • \(\frac{2}{3}⋅\frac{5}{7}\)
  • \(\frac{1}{5}⋅\frac{4}{8}\)
  • \(\frac{1}{2}⋅\frac{1}{3}\)
  • \(\frac{3}{4}⋅\frac{20}{9}\)
  • \(\frac{5}{7}⋅\frac{49}{10}\)
  • \(\frac{2}{3}⋅\frac{9}{12}\)
  • \(\frac{6}{14}⋅\frac{21}{12}\)
  • \(\frac{44}{15}⋅\frac{15}{11}\)
  • \(3 \frac{3}{4} \cdot 2 \frac{1}{3}\)
  • \(2\frac{7}{10}⋅5\frac{5}{6}\)
  • \(\frac{3}{11}(−\frac{5}{2})\)
  • \(-\frac{4}{5}(\frac{9}{5})\)
  • \((−\frac{9}{5} (−\frac{3}{10}) \)
  • \(\frac{6}{7}(−\frac{14}{3})\)
  • \((−\frac{9}{12})(−\frac{4}{8})\)
  • \(−\frac{3}{8}(−\frac{4}{15})\)
  • \(\frac{1}{7}⋅\frac{1}{2}⋅\frac{1}{3}\)
  • \(\frac{3}{5}⋅\frac{15}{21}⋅\frac{7}{27}\)
  • \(\frac{2}{5}⋅3\frac{1}{8}⋅\frac{4}{5}\)
  • \(2\frac{4}{9}⋅\frac{2}{5}⋅2\frac{5}{11}\)

1: \(10/21\)

11: \(−15/22\)

13:\(27/50\)

15: \(3/8\)

17: \(1/42\)

Exercise \(\PageIndex{5}\)

Determine the reciprocal of the following numbers.

  • \(\frac{1}{2}\)
  • \(\frac{8}{5}\)
  • \(−\frac{2}{3}\)
  • \(−\frac{4}{3}\)
  • \(−4\)
  • \(2\frac{1}{3}\)
  • \(1\frac{5}{8}\)

3: \(−3/2\)

5: \(1/10\)

Exercise \(\PageIndex{6}\)

Divide and reduce to lowest terms.

  • \(\frac{1}{2} \div \frac{2}{3}\)
  • \(\frac{5}{9} \div \frac{1}{3}\)
  • \(\frac{5}{8} \div (−\frac{4}{5})\)
  • \((−\frac{2}{5})÷\frac{15}{3}\)
  • \(\dfrac{−\frac{6}{7}}{−\frac{6}{7}}\)
  • \(\dfrac{−\frac{1}{2}}{\frac{1}{4}}\)
  • \(\dfrac{−\frac{10}{3}}{−\frac{5}{20}}\)
  • \(\dfrac{\frac{2}{3}}{\frac{9}{2}}\)
  • \(\dfrac{\frac{30}{50}}{\frac{5}{3}}\)
  • \(\dfrac{\frac{1}{2}}{2}\)
  • \(\dfrac{5}{\frac{2}{5}}\)
  • \(\dfrac{−6}{\frac{5}{4}}\)
  • \(2 \frac{1}{2} \div \frac{5}{3}\)
  • \(4 \frac{2}{3} \div 3 \frac{1}{2}\)
  • \(5 \div 2\frac{3}{5}\)
  • \(4\frac{3}{5} \div 23\)

3: \(−25/32\)

7: \(40/3\)

9: \(9/25\)

11: \(25/2\)

13: \(1 \frac{1}{2}\)

15: \(1 \frac{12}{13}\)

Exercise \(\PageIndex{7}\)

Add or subtract and reduce to lowest terms.

  • \(\frac{17}{20}-\frac{5}{20}\)
  • \(\frac{4}{9}-\frac{13}{9}\)
  • \(\frac{3}{5}+\frac{1}{5}\)
  • \(\frac{11}{15}+\frac{9}{15}\)
  • \(\frac{5}{7}-2\frac{1}{7}\)
  • \(\frac{1}{2}+\frac{1}{3}\)
  • \(\frac{1}{5}-\frac{1}{4}\)
  • \(\frac{3}{4}-\frac{5}{2}\)
  • \(\frac{3}{8}+\frac{7}{16}\)
  • \(\frac{7}{15}-\frac{3}{10}\)
  • \(\frac{3}{10}+\frac{2}{14}\)
  • \(\frac{2}{30}+\frac{5}{21}\)
  • \(\frac{3}{18}-\frac{1}{24}\)
  • \(5 \frac{1}{2}+2\frac{1}{3}\)
  • \(1 \frac{3}{4}+2 \frac{1}{10}\)
  • \(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)
  • \(\frac{2}{3}+\frac{3}{5}-\frac{2}{9}\)
  • \(\frac{7}{3}-\frac{3}{2}+\frac{2}{15}\)
  • \(\frac{9}{4}-\frac{3}{2}+\frac{3}{8}\)
  • \(\frac{2}{3}-4\frac{1}{2}+3\frac{1}{6}\)
  • \(1-\frac{6}{16}+\frac{3}{18}\)
  • \(3-\frac{1}{21}-\frac{1}{15}\)

5: \(−1 \frac{3}{7}\)

9: \(−7/4\)

11: \(1/6\)

13: \(32/105\)

15: \(7 \frac{5}{6}\)

19: \(29/30\)

21: \(2 \frac{2}{3}\)

23: \(19/24\)

Exercise \(\PageIndex{8}\)

Perform the operations. Reduce answers to lowest terms.

  • \(\frac{3}{14} \cdot \frac{7}{3} \div \frac{1}{8}\)
  • \(\frac{1}{2} \cdot (-\frac{4}{5}) \div \frac{14}{15}\)
  • \(\frac{1}{2} \div \frac{3}{4} \cdot \frac{1}{5}\)
  • \(-\frac{5}{9} \div \frac{5}{3} \cdot \frac{5}{2}\)
  • \(\frac{4}{5} \div 4 \cdot \frac{1}{2}\)
  • \(\frac{5}{3} \div 15 \cdot \frac{2}{3}\)
  • What is the product of \(\frac{3}{16}\) and \(\frac{4}{9}\)?
  • What is the product of \(−\frac{24}{5}\) and \(\frac{25}{8}\)?
  • What is the quotient of \(\frac{5}{9}\) and \(\frac{25}{3}\)?
  • What is the quotient of \(−\frac{16}{5}\) and \(32\)?
  • Subtract \(\frac{1}{6}\) from the sum of \(\frac{9}{2}\) and \(\frac{2}{3}\).
  • Subtract \(\frac{1}{4}\) from the sum of \(\frac{3}{4}\) and \(\frac{6}{5}\).
  • What is the total width when \(3\) boards, each with a width of \(2 \frac{5}{8}\) inches, are glued together?
  • The precipitation in inches for a particular 3-day weekend was published as \(\frac{3}{10}\) inches on Friday, \(1\frac{1}{2}\) inches on Saturday, and \(\frac{3}{4}\) inches on Sunday. Calculate the total precipitation over this period.
  • A board that is \(5\frac{1}{4}\) feet long is to be cut into \(7\) pieces of equal length. What is length of each piece?
  • How many \(\frac{3}{4}\) inch thick notebooks can be stacked into a box that is \(2\) feet high?
  • In a mathematics class of \(44\) students, one-quarter of the students signed up for a special Saturday study session. How many students signed up?
  • Determine the length of fencing needed to enclose a rectangular pen with dimensions \(35\frac{1}{2}\) feet by \(20\frac{2}{3}\) feet.
  • Each lap around the track measures \(\frac{1}{4}\) mile. How many laps are required to complete a \(2\frac{1}{2}\) mile run?
  • A retiree earned a pension that consists of three-fourths of his regular monthly salary. If his regular monthly salary was \($5,200\), then what monthly payment can the retiree expect from the pension plan?

3: \(2/15\)

5: \(9/28\)

7: \(1/10\)

9: \(1/12\)

11: \(1/15\)

15: \(7 \frac{7}{8}\) inches

17: \(\frac{3}{4}\) feet

19: \(11\) students

21: \(10\) laps

Discussion Board Topics

  • Does \(0\) have a reciprocal? Explain.
  • Explain the difference between the LCM and the GCF. Give an example.
  • Explain the difference between the LCM and LCD.
  • Why is it necessary to find an LCD in order to add or subtract fractions?
  • Explain how to determine which fraction is larger, \(\frac{7}{16}\) or \(\frac{1}{2}\).
  • EXPLORE Random Article

How to Check Math Homework

Last Updated: May 10, 2021 References

This article was co-authored by Sean Alexander, MS . Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed 14,714 times.

Most people who work hard on their homework want to make sure that they are doing it correctly. When you are working from home, however, you don’t have your teacher to tell you whether or not your answers are correct. There are a number of ways to check math work you do outside of school. By checking your own work, having someone else check your work, or using online tools, you can make sure your solutions are correct before turning in your work.

Checking By Yourself

Step 1 Estimate.

  • If you are doing multiplication, you can check your work by doing repeated addition.

Asking for Help

Step 1 Ask your parents.

  • Some good sites for going over how to do math problems quickly are Math is Fun [5] X Research source and Virtual Nerd. [6] X Research source

Step 2 Compare answers with friends.

  • When you compare your answer with a friend, make sure you are not just changing your answers without learning where you made your mistake. If your friend found the correct answer, have him or her show you how to solve the problem.

Step 3 Talk to your teacher.

  • If you do your work at home but don’t feel confident about it, talk to your teacher as soon as possible the next day. They can quickly check your work, and you might have time to correct your answers before turning it in. Likely, you will get credit for trying your best.

Using Resources

Step 1 Use a calculator.

  • Work through your problems first, and only use the calculator to check your answers. You need to show your work so that your teacher knows you understand how to solve the problems.
  • If you don’t have a calculator, you can find a number of online calculators by simply searching for them on Google.

Step 2 Use online tools.

  • For algebra, you can use an equation calculator, like Symbolab. [7] X Research source
  • For geometry, you can simply type what you are looking for into Google, and a calculator will pop up. For example, if you are finding the area of a triangle, type “area of a triangle” into Google. Then insert your known values into the calculator (such as base and height), and Google will supply the answer.
  • There are a number of converters online. Math is Fun has a unit converter that can help you convert from one unit of measurement to another, such as inches to centimeters. [8] X Research source Convert Me has conversion calculators for most measurements, including speed, temperature, and capacity. [9] X Research source

Step 3 Use the back of your textbook.

  • As when using a calculator or online tools, try doing the problems on your own first, then check your answers.

Expert Q&A

Video . by using this service, some information may be shared with youtube..

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Ask for Feedback

  • ↑ Sean Alexander, MS. Academic Tutor. Expert Interview. 14 May 2020.
  • ↑ http://mathandreadinghelp.org/how_to_estimate_a_math_problem.html
  • ↑ http://www.virtualnerd.com/middle-math/equations-functions/expressions/inverse-operations-definition
  • ↑ http://www.futurity.org/learning-students-teaching-741342/
  • ↑ http://mathisfun.com/
  • ↑ http://www.virtualnerd.com/
  • ↑ https://www.symbolab.com/solver/equation-calculator
  • ↑ https://www.mathsisfun.com/unit-conversion-tool.php
  • ↑ http://www.convert-me.com/en/

About this article

Sean Alexander, MS

To check your math homework yourself, try plugging your answer back into the equation you started with. For example, if you solved for x, plug the value you got for x into the equation and check to see if the equation makes sense. If it doesn't, you know there's something off about your answer. Another way you can check your work is by using an alternative method to solve the problem. If you get the same answer using a different method, there's a good chance your original answer was right. For example, if you're trying to solve 45×3, you could also solve the problem using addition by adding 45+45+45 to get 135. If 135 is the answer you got using multiplication, you know your answer is correct. For more expert math-checking tips, read the full article below! Did this summary help you? Yes No

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Equivalent Fractions Worksheets

Every nook and cranny of our pdf equivalent fractions worksheets is stuffed with practice that helps children ease into fractions equivalence! As concepts like operations with fractions and comparing or ordering them are all built around equivalence of fractions, a deeper insight into the topic will alleviate the learning stress of students in grade 3, grade 4, and grade 5. The printable resources include determining whether a fraction is equivalent or not, identifying equivalent fractions, generating equivalent fractions, and answering Who-Am-I riddles and patterns. Try some of our free equivalent fraction worksheets now!

» Equivalent Fractions on a Number Line

» Equivalent Fractions | Visual Models

Equivalent or Not Equivalent?

Equivalent or Not Equivalent?

Is 4/6 equivalent to 2/3? Yes, it is. Find similar pairs of fractions in these pdf worksheets on equivalent fractions, ascertain whether they are equivalent or not, and write a '=' or '≠' symbol in between accordingly.

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Step-by-Step | Multiplication

Finding Equivalent Fractions Step-by-Step

Are your 3rd grade and 4th grade children aware of the steps in finding an equivalent fraction? Let them know that both multiplication and division are the bread and butter of equivalent fractions.

Missing Parts | Standard - Easy

Missing Parts of Fractions | Standard

Missing here is either the numerator or denominator of a fraction, equivalent to another. Find out the factor that makes it equivalent to the given fraction, and fill in the missing part.

easy 1

Missing Parts of Fractions | Variables

A variable is given in place of the missing parts of an equivalent-fraction sentence. There's a shortcut to solving these problems. All you need to do is cross-multiply the fractions and find the missing value.

Multiple Equivalent Fractions | Increasing

Missing Parts of Multiple Equivalent Fractions

Pound it into 4th grade and 5th grade students' heads that a fraction can have an infinite number of equivalent fractions, and task them with finding the missing parts of more than five equivalents for a fraction.

Identifying and Generating Equivalent Fractions

Identifying and Generating Equivalent Fractions

Scoop up our printable equivalent fractions worksheets, ideal for grade 3 and grade 4, with practice exercises on identifying equivalent fractions in part A and generating three equivalents for a fraction in part B.

Who Am I? | Type 1

Get children excitedly enthusing over this set of riddles! Pore over the sentences, frame the equivalent-fraction statement, and figure out the fraction that replaces "I" in each and every riddle.

Circling the Equivalent Fractions

Circling the Equivalent Fractions

Buff up your practice with our pdf equivalent fractions worksheets, which require grade 4 and grade 5 children to circle three to four fractions out of a set of five that are equivalent to a given fraction.

Patterns | Easy

Equivalent Fractions Patterns

As fun and frolic as they are, patterns are not fully devoid of challenge! Seize this compilation of printable worksheets, analyze the patterns the fractions follow, and fill in the blanks with the appropriate fraction.

Equivalent Fractions on a Number Line

Equivalent Fractions on a Number Line

Did you know that equivalent fractions represent the same point on a number line? Work out our printable worksheets and learn such intriguing facts by plotting equivalent fractions on number lines.

(15 Worksheets)

Equivalent Fractions - Visual Models

Equivalent Fractions - Visual Models

Jam-packed with visual models like fraction pies, pizzas, 2d shapes split equally, area models, and tape diagrams, this pdf practice set will help children chase away all their doubts in fraction equivalence.

(48 Worksheets)

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Do you need help with your homework? Do you want to learn new things and improve your grades? If so, you'll love our app! The Magic Math - AI Math Solver is the ultimate learning companion for students of all ages and levels. Whether you need help with math, science, history, or any other subjects, our app has you covered. Just scan any question or problem with your camera and get instant answers and explanations from our smart AI tutor. HOW IT WORKS You can solve any math problem and homework with our AI math solver and homework help tool. Just use your camera to scan the problem, write it on the screen, or type it in our calculator. The tool will give you the answer right away, along with detailed step-by-step explanations. You can learn how to solve any math problem and any subject with our application. KEY FEATURES - AI homework solves all subjects (Math, Physics, Chemistry, Biology, Geography, English, French, and so on) - Scan and solve any question or problem in seconds - Learn from detailed step-by-step solutions and clear explanations - Explore a variety of subjects and topics - Smart calculator for iPhone or iPad with Basic, scientific, or fraction calculators SOLVE ANY SUBJECTS IN ONE APP - Math (Mathématiques, matemáticas...) - Physics - Chemistry - Biology - Geography - English (TOEIC, TOEFL, IELTS, CEFR, SAT, etc.)/French (DELF, DALF, etc.) ... WIDE RANGE OF MATH TOPICS COVERED - Function (Linear, Quadratic, Polynomial, Exponential, Rational, Logarithmic, Inverse Function) - Algebra (Real Number, Arithmetic, Set theory, Expression, Logarithm, Complex Number) - Trigonometry (Trigonometric Ratios, Law of Sines, Law of Cosines, Reciprocal Properties) - Sequences (Identifying sequences, Series, Recursive and Explicit form, Tests for Convergence) - Geometry (Plane & Solid Geometry, Algebra & lines, Lines & Planes in Space, Transformation) - Calculus (Limits, Derivatives, Integrals, Tangent lines, Area below a curve, Identifying Conics, Rotations of Conics, Differential equations) - Statistics and Data Analysis (Probability; Data Representation, Poisson/Normal Distribution) - Matrix (Matrix Algebra, System of Linear Equations, & Matrices) LANGUAGE SUPPORT You can also choose your preferred language, as Math Solver supports English, Chinese, French, German, Hindi, Italian, Japanese, Portuguese, Russian, Spanish, and more. Download Magic Math - AI Math Solver right now! Privacy Policy: https://sites.google.com/easytool.io/privacypolicy Terms Of Use: https://sites.google.com/easytool.io/termofservice Support: [email protected]

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Smart Classroom Management

A Simple, Effective Homework Plan For Teachers: Part 1

So for the next two weeks I’m going to outline a homework plan–four strategies this week, four the next–aimed at making homework a simple yet effective process.

Let’s get started.

Homework Strategies 1-4

The key to homework success is to eliminate all the obstacles—and excuses—that get in the way of students getting it done.

Add leverage and some delicately placed peer pressure to the mix, and not getting homework back from every student will be a rare occurrence.

Here is how to do it.

1. Assign what students already know.

Most teachers struggle with homework because they misunderstand the narrow purpose of homework, which is to practice what has already been learned. Meaning, you should only assign homework your students fully understand and are able to do by themselves.

Therefore, the skills needed to complete the evening’s homework must be thoroughly taught during the school day. If your students can’t prove to you that they’re able to do the work without assistance, then you shouldn’t assign it.

It isn’t fair to your students—or their parents—to have to sit at the dinner table trying to figure out what you should have taught them during the day.

2. Don’t involve parents.

Homework is an agreement between you and your students. Parents shouldn’t be involved. If parents want to sit with their child while he or she does the homework, great. But it shouldn’t be an expectation or a requirement of them. Otherwise, you hand students a ready-made excuse for not doing it.

You should tell parents at back-to-school night, “I got it covered. If ever your child doesn’t understand the homework, it’s on me. Just send me a note and I’ll take care of it.”

Holding yourself accountable is not only a reminder that your lessons need to be spot on, but parents will love you for it and be more likely to make sure homework gets done every night. And for negligent parents? It’s best for their children in particular to make homework a teacher/student-only agreement.

3. Review and then ask one important question.

Set aside a few minutes before the end of the school day to review the assigned homework. Have your students pull out the work, allow them to ask final clarifying questions, and have them check to make sure they have the materials they need.

And then ask one important question: “Is there anyone, for any reason, who will not be able to turn in their homework in the morning? I want to know now rather than find out about it in the morning.”

There are two reasons for this question.

First, the more leverage you have with students, and the more they admire and respect you , the more they’ll hate disappointing you. This alone can be a powerful incentive for students to complete homework.

Second, it’s important to eliminate every excuse so that the only answer students can give for not doing it is that they just didn’t care. This sets up the confrontation strategy you’ll be using the next morning.

4. Confront students on the spot.

One of your key routines should be entering the classroom in the morning.

As part of this routine, ask your students to place their homework in the top left-hand (or right-hand) corner of their desk before beginning a daily independent assignment—reading, bellwork , whatever it may be.

During the next five to ten minutes, walk around the room and check homework–don’t collect it. Have a copy of the answers (if applicable) with you and glance at every assignment.

You don’t have to check every answer or read every portion of the assignment. Just enough to know that it was completed as expected. If it’s math, I like to pick out three or four problems that represent the main thrust of the lesson from the day before.

It should take just seconds to check most students.

Remember, homework is the practice of something they already know how to do. Therefore, you shouldn’t find more than a small percentage of wrong answers–if any. If you see more than this, then you know your lesson was less than effective, and you’ll have to reteach

If you find an assignment that is incomplete or not completed at all, confront that student on the spot .

Call them on it.

The day before, you presented a first-class lesson and gave your students every opportunity to buzz through their homework confidently that evening. You did your part, but they didn’t do theirs. It’s an affront to the excellence you strive for as a class, and you deserve an explanation.

It doesn’t matter what he or she says in response to your pointed questions, and there is no reason to humiliate or give the student the third degree. What is important is that you make your students accountable to you, to themselves, and to their classmates.

A gentle explanation of why they don’t have their homework is a strong motivator for even the most jaded students to get their homework completed.

The personal leverage you carry–that critical trusting rapport you have with your students–combined with the always lurking peer pressure is a powerful force. Not using it is like teaching with your hands tied behind your back.

Homework Strategies 5-8

Next week we’ll cover the final four homework strategies . They’re critical to getting homework back every day in a way that is painless for you and meaningful for your students.

I hope you’ll tune in.

If you haven’t done so already, please join us. It’s free! Click here and begin receiving classroom management articles like this one in your email box every week.

What to read next:

  • A Powerful Way To Relieve Stress: Part One
  • The Best Time To Review Your Classroom Management Plan
  • Why Your New Classroom Management Plan Isn't Working
  • A Simple Exercise Program For Teachers
  • How To Make A Warning Most Effective

20 thoughts on “A Simple, Effective Homework Plan For Teachers: Part 1”

Good stuff, Michael. A lot of teachers I train and coach are surprised (and skeptical) at first when I make the same point you make about NOT involving parents. But it’s right on based on my experience as a teacher, instructional coach, and administrator the past 17 years. More important, it’s validated by Martin Haberman’s 40 years of research on what separates “star” teachers from “quitter/failure” teachers ( http://www.habermanfoundation.org/Book.aspx?sm=c1 )

I love the articles about “homework”. in the past I feel that it is difficuty for collecting homework. I will try your plan next year.

I think you’ll be happy with it, Sendy!

How do you confront students who do not have their homework completed?

You state in your book to let consequences do their job and to never confront students, only tell them the rule broken and consequence.

I want to make sure I do not go against that rule, but also hold students accountable for not completing their work. What should I say to them?

They are two different things. Homework is not part of your classroom management plan.

Hi Michael,

I’m a first-year middle school teacher at a private school with very small class sizes (eight to fourteen students per class). While I love this homework policy, I feel discouraged about confronting middle schoolers publicly regarding incomplete homework. My motive would never be to humiliate my students, yet I can name a few who would go home thinking their lives were over if I did confront them in front of their peers. Do you have any ideas of how to best go about incomplete homework confrontation with middle school students?

The idea isn’t in any way to humiliate students, but to hold them accountable for doing their homework. Parts one and two represent my best recommendation.:)

I believe that Homework is a vital part of students learning.

I’m still a student–in a classroom management class. So I have no experience with this, but I’m having to plan a procedure for my class. What about teacher sitting at desk and calling student one at a time to bring folder while everyone is doing bellwork or whatever their procedure is? That way 1) it would be a long walk for the ones who didn’t do the work :), and 2) it would be more private. What are your thoughts on that? Thanks. 🙂

I’m not sure I understand your question. Would you mind emailing me with more detail? I’m happy to help.

I think what you talked about is great. How do you feel about flipping a lesson? My school is pretty big on it, though I haven’t done it yet. Basically, for homework, the teacher assigns a video or some other kind of media of brand new instruction. Students teach themselves and take a mini quiz at the end to show they understand the new topic. Then the next day in the classroom, the teacher reinforces the lesson and the class period is spent practicing with the teacher present for clarification. I haven’t tried it yet because as a first year teacher I haven’t had enough time to make or find instructional videos and quizzes, and because I’m afraid half of my students will not do their homework and the next day in class I will have to waste the time of the students who did their homework and just reteach what the video taught.

Anyway, this year, I’m trying the “Oops, I forgot my homework” form for students to fill out every time they forget their homework. It keeps them accountable and helps me keep better track of who is missing what. Once they complete it, I cut off the bottom portion of the form and staple it to their assignment. I keep the top copy for my records and for parent/teacher conferences.

Here is an instant digital download of the form. It’s editable in case you need different fields.

Thanks again for your blog. I love the balance you strike between rapport and respect.

Your site is a godsend for a newbie teacher! Thank you for your clear, step-by-step, approach!

I G+ your articles to my PLN all the time.

You’re welcome, TeachNich! And thank you for sharing the articles.

Hi Michael, I’m going into my first year and some people have told me to try and get parents involved as much as I can – even home visits and things like that. But my gut says that negligent parents cannot be influenced by me. Still, do you see any value in having parents initial their student’s planner every night so they stay up to date on homework assignments? I could also write them notes.

Personally, no. I’ll write about this in the future, but when you hold parents accountable for what are student responsibilities, you lighten their load and miss an opportunity to improve independence.

I am teaching at a school where students constantly don’t take work home. I rarely give homework in math but when I do it is usually something small and I still have to chase at least 7 kids down to get their homework. My way of holding them accountable is to record a homework completion grade as part of their overall grade. Is this wrong to do? Do you believe homework should never be graded for a grade and just be for practice?

No, I think marking a completion grade is a good idea.

I’ve been teaching since 2014 and we need to take special care when assigning homework. If the homework assignment is too hard, is perceived as busy work, or takes too long to complete, students might tune out and resist doing it. Never send home any assignment that students cannot do. Homework should be an extension of what students have learned in class. To ensure that homework is clear and appropriate, consider the following tips for assigning homework:

Assign homework in small units. Explain the assignment clearly. Establish a routine at the beginning of the year for how homework will be assigned. Remind students of due dates periodically. And Make sure students and parents have information regarding the policy on missed and late assignments, extra credit, and available adaptations. Establish a set routine at the beginning of the year.

Thanks Nancie L Beckett

Dear Michael,

I love your approach! Do you have any ideas for homework collection for lower grades? K-3 are not so ready for independent work first thing in the morning, so I do not necessarily have time to check then; but it is vitally important to me to teach the integrity of completing work on time.

Also, I used to want parents involved in homework but my thinking has really changed, and your comments confirm it!

Hi Meredith,

I’ll be sure and write about this topic in an upcoming article (or work it into an article). 🙂

Leave a Comment Cancel reply

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  • Math Article

Equivalent Fractions

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent fractions, because they both are equal to the ½. A fraction is a part of a whole. Equivalent fractions represent the same portion of the whole. 

For each fraction, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we have to find the third equivalent fraction of ⅔; then we have to multiply 2/3 by 3/3. Hence, 2/3 × (3/3) = 6/9, is the fraction equivalent to 2/3. 

What are Equivalent Fractions?

Equivalent fractions state that two or more than two fractions are said to be equal if both results the same fraction after simplification. Let us say, a/b and c/d are two fractions, after the simplification of these fractions, both result in equivalent fractions, say e/f, then they are equal to each other.

For example, the equivalent fraction of 1/3 is 5/15, because if we simplify 5/15, then the resulted fraction is the same.

Equivalent Fractions example

The biggest question here can be, why do they have equal values in spite of having different numbers?

The answer to this question is that, as the numerator and denominator are not co-prime numbers, therefore they have a common multiple, which on division gives exactly the same value.

Example of Equivalent Fraction

Take for an example:

1/2 = 2/4 = 4/8

But, it is clearly seen that the above fractions have different numerators and denominators.

Dividing both numerator and denominator by their common factor, we have:

In the same way, if we simplify 2/4, again get 1/2.

Equivalent fractions of a mixed fraction:

Let us consider a mixed fraction to find its equivalent fraction.

Mixed fraction = 1 ½

Now, convert this fraction into an improper fraction.

1 ½ = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2

The equivalent fractions for the above fraction are:

3/2 = (3 × 2)/(2 × 2) = 6/4

3/2 = (3 × 3)/(2 × 3) = 9/6

3/2 = (3 × 4)/(2 × 4) = 12/8 and so on.

How to Find Equivalent Fractions?

Equivalent fractions are evaluated by multiplying or dividing both the numerator and the denominator by the same number. Therefore, equivalent fractions, when reduced to their simplified value, will all be the same.

Multiplying numerator and denominator by the same number

For example, consider the fraction 1/5

  • Multiplying numerator and denominator with 2, we get 1/5 × 2/2 = 2/10
  • Multiplying numerator and denominator with 3, we get 1/5 × 3/3 = 3/15
  • Multiplying numerator and denominator with 4, we get 1/5 × 4/4 = 4/20

Therefore, we can conclude that,

1/5 = 2/10 = 3/15 = 4/20

Dividing numerator and denominator by the same number

For example, we need to find the equivalent fraction of 18/32.

Find the Highest common factor of 18 and 32.

HCF (18, 32) = 2

Now divide the numerator and denominator by 2, to get the equivalent fraction of 18/32.

(18 ÷2)/(32÷2) = 9/16

Hence, 9/16 is equivalent to 18/32.

Note:  We can only multiply or divide by the same numbers to get an equivalent fraction and not addition or subtraction. Simplification to get equivalent numbers can be done to a point where both the numerator and denominator should still be whole numbers.

Equivalent Fractions Chart

Let us see the equivalent fractions for unit fractions.

Methods to Determine Equivalent Fractions

How can we determine if two fractions are equivalent or not? It is possible by these methods:

  • Method 1: Make the Denominators the same
  • Method 2: Cross Multiply
  • Method 3: Convert to decimals

By making the denominators the same, we can evaluate if two fractions are equivalent.

For example, find if 2/3 and 6/9 are equivalent.

LCM of 3 and 9 = 9

Multiply 2/3 by 3/3 to make the denominator equal to 9.

2/3 × 3/3 = 6/9

Hence, by making the denominators the same, we can see, 2/3 and 6/9 are equivalent fractions.

Given, two fractions 1/2 and 3/6

Cross multiply both the fractions to get:

Equivalent fraction - Cross multiplication method

Since, both the values are equal, therefore, 1/2 and 3/6 are equivalent fractions.

If two fractions are given, we can simply find their decimals to check if they are equivalent fractions.

Let us check if 1/4 and 3/12 are equivalent fractions by converting them in decimal form.

3/12 = 0.25

Since, both the fractions result in the same decimal, thus they are equivalent.

Solved Examples

Example 1: The given fractions 5/16 and x/12 are equivalent fractions, then find the value of x.

Given:  5/16 = x/12

x = (5 × 12)/16

Therefore, the value of x is 15/4.

Example 2: Two fractions 3/5 and 4/x are equivalent. Find the value of x.

Solution: Given,

x = (4 × 5)/3

Example 3: What fractions are the same as ¼?

Solution: To find equivalent fractions of ¼ we need to multiply the numerator and denominator by the same numbers. Hence,

¼ × (2/2) = 2/8

¼ × (3/3) = 3/12

¼ × (4/4) = 4/16

¼ × (5/5) = 5/20

Video Lesson on Fractions

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Practice Questions

  • Find the equivalent fraction of 8/10
  • What is the simplest form of 9/81?
  • Write the fraction three-sevenths as an equivalent fraction with a denominator of 21.
  • Write the fraction five-eighth as an equivalent fraction with a denominator of 24.

Related Articles

Frequently asked questions on equivalent fractions, what are equivalent fractions, what are the examples of equivalent fractions, how to determine whether fractions are equivalent, what is the equivalent fraction of ⅗, what are the equivalent fractions of 5/10.

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check fraction homework

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Hi, yes please. Can you do it for 8/9?

The equivalent fraction to 8/9 is 16/18

how did you find it please teach me?

Multiply numerator and denominator by a common factor, to get the equivalent fractions. (8/9) x (2/2) (8×2)/(9×2) 16/18

what is equal to 1/5?

2/10 is equivalent to 1/5

What is equivalent to 7/12 because I’m in fifth grade

Multiply the fraction 7/12 by any natural number both in numerator and denominator to get its equivalent. For example, (7/12) * (3/3) = 21/36

what is equivalent to 1/10

2/20,3/30, etc.

What is equivalent to 4/5

Multiply 4/5 with 2/2 to get: 8/10. Thus, 8/10 is equivalent to 4/5

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  23. A Simple, Effective Homework Plan For Teachers: Part 1

    Here is how to do it. 1. Assign what students already know. Most teachers struggle with homework because they misunderstand the narrow purpose of homework, which is to practice what has already been learned. Meaning, you should only assign homework your students fully understand and are able to do by themselves.

  24. Equivalent Fractions

    For each fraction, we can find its equivalent fraction by multiplying both numerator and denominator with the same number. For example, we have to find the third equivalent fraction of ⅔; then we have to multiply 2/3 by 3/3. Hence, 2/3 × (3/3) = 6/9, is the fraction equivalent to 2/3. Table of contents: Definition Examples