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Division Worksheets

Welcome to the division worksheets page at Math-Drills.com! Please give us your undivided attention while we introduce this page. Our worksheets for division help you to teach students the very important concept of division. If students have a good recall of multiplication facts, the division facts should be a breeze to teach. If you want your students to experience success in learning division, please make sure they know their multiplication facts to 81, how to multiply by 0 and how to multiply by 10. If they don't know these things, learning division will take a lot longer.

On this page you will find many Division Worksheets including division facts and long division with and without remainders. We start off with some division facts which are just the multiplication facts expressed in a different way. The main difference is that you can't divide by 0 and get a real number. If you really want your students to impress, say at their dinner table when their parents ask them what they learned today, you can teach them that division by zero is undefined.

The rest of the page is devoted to long division which for some reason is disliked among some members of the population. Long division is most difficult when students don't know their multiplication facts, so make sure they know them first! Oh, we already said that. What about a long division algorithm... maybe the one you or your parents or your grandparents learned? We adamantly say, yes! The reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals and whole numbers. Long division really isn't that hard.

Most Popular Division Worksheets this Week

Division Tables

Division facts tables with individual questions.

Like their counterparts on the multiplication facts page, these division facts tables can be used in a variety of ways to help students learn division facts. Students can memorize, look for patterns in the tables, compare them to multiplication tables, write answers on the versions with the answers omitted, or a variety of other learning activities. The tables come in gray, color and Montessori color depending on what fits you and your printer or school the best. For those that have already mastered the facts up to 12, they might be challenged to try the 13 to 24 versions.

Division Facts up to the 7 Times Table

Division facts up to the 7 times table (vertical).

If your students aren't quite ready for all of the division facts at once, this might be a good place to start. Perhaps they are really good at the multiplying up to 5; there is a worksheet to help them practice, and when they are ready, they can include 6 then 7. This section includes vertical questions with the traditional division symbol (aka bracket) and some arranged with a division symbol like you might see addition, subtraction or multiplication arranged.

Division Facts up to the 7 Times Table (Horizontal)

More worksheets with division facts up to 7, but these ones are arranged horizontally. This is a more natural arrangement for students who are used to reading things from left to right, allows them to practice recalling the answers and it is possible to fit 100 of these questions on the page without it getting too cluttered. If clutter is a problem though, there are also 50 and 25 question options.

Dividing Individual Facts up the the 7 Times Table (Vertically)

Some students require chunking and more practice before they can handle the more complex pages with many different divisors. Here the worksheets only contain one divisor and there are several repetitions of the set on each page.

Dividing Individual Facts up the the 7 Times Table (Horizontally)

More individual division facts worksheets but with a horizontal arrangement. This section includes 50 and 25 question options with each set repeated on the page.

Division Facts up to the 9 Times Table

Division facts up to the 9 times table (vertical).

Manipulatives can help students "get" the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles. For the question 81 ÷ 9, students would start with eight ten blocks and one unit block. They would trade in the ten blocks for unit blocks and try to distribute all 81 of the unit blocks into nine piles. If they did it correctly, they would end up with 9 piles of 9 units and could say that 81 ÷ 9 = 9 as there are 9 units in each pile.

Division Facts up to the 9 Times Table (Horizontal)

If students learn up to the 9 times table and can do all the related division, they are likely to do well in later math studies. Long multiplication and long division, algebra, and many other math topics rely on students knowing these facts. Division facts worksheets up to the nine times tables can be used for students to practice, as a diagnostic test to see what gaps exist, or as a mastery test before moving on to the next topic. This section includes horizontally arranged questions which allows for a 100 per page option. Worksheets up to the 8 times table are also included to ensure a continual flow with the rest of this page, say, if you were adding one number at a time.

Dividing Individual Facts up the the 9 Times Table (Vertically)

More individual facts where a single number is used as the divisor throughout the entire worksheet. The quotients end up being in the range 1 to 9. These are great for students that need more practice on one or more divisors. This might be identified using a diagnostic test of a worksheet that includes all the division facts. If students consistently get questions wrong with a certain divisor, these worksheets might help them.

Dividing Individual Facts up the the 9 Times Table (Horizontally)

Same as the previous section except with horizontally arranged questions and more options for the number of questions per page.

Division Facts up to the 10 Times Table

Division facts up to the 10 times table (vertical).

Ten is such an important number in math. Our entire numbering system is based on tens. There are ten digits and each lower place is a tenth (divided by 10) of the place before it. Although 10 is a two-digit number, it is almost always included in multiplication and division facts learning. Multiplying and dividing by 10 is so important there is a whole page (powers of ten) on Math-Drills dedicated to it.

If you jumped right to this section, you cannot be blamed! A lot of students learn their times tables all at once and that means including the most important 10! So, when they are ready for division worksheets, they are ready for this section. For students who might be struggling a bit though, please scroll up and start them off with something a little more at their pace.

Division Facts up to the 10 Times Table (Horizontal)

Even with its size, 10 is often the easiest divisor to use... well, besides 1. This section includes horizontally arranged practice questions for all the division facts from the 1 times to the 10 times table.

Dividing Individual Facts up the the 10 Times Table (Vertically)

The worksheets in this section are included for students that need the facts one at a time with quotients from 1 to 10.

Dividing Individual Facts up the the 10 Times Table (Horizontally)

A horizontal repeat of the previous section.

Division Facts up to the 12 Times Table

Division facts up to the 12 times table (vertical).

Ah, twelve. Educators have a penchant for the the 12 times table likely because it is important in clocks, eggs, the Vendergood language, and definitely to the Dozenal Societies of America and Great Britain. In mathematics, it is seen mostly in the completion of both multiplication and division facts worksheets. Since Math-Drills is happy to support the base twelve system, we present worksheets with division facts up to the 12 times table in the unlikely event that the duodecimal (aka dozenal) system is ever adopted.

Division Facts up to the 12 Times Table (Horizontal)

Division is essentially asking the question, "How many _____'s are in _____?" For the question, 81 ÷ 9, the prompt would sound like, "How many 9's are in 81?" This prompt will benefit students in later math studies when there are more complex concepts such as dividing decimals or fractions. "How many thirds are in four?" or even better, "How many third cups are in four cups?" If necessary, get out the measuring cups.

This important section includes worksheets with division facts up to the 12 times table with a 100 question option.

Dividing Individual Facts up the the 12 Times Table (Vertically)

So, if you are having your students learn division facts up to the 12 times table, it might be useful to have some worksheets with individual facts for a few students who might be overwhelmed with everything at once!

Dividing Individual Facts up the the 12 Times Table (Horizontally)

Same idea as the previous section, but with a horizontal arrangement and different numbers of questions on each page.

Division Facts beyond the 12 Times Table

Division facts beyond the 12 times table (vertical).

Scenario: you have some students that have aced the division facts up to the 12 times table and need more of a challenge. This section has got you covered. Is there an argument for learning division facts for times tables beyond 9? 10? 12? Sure, why not. Students are likely to apply their knowledge in future math studies by instantly recognizing that the square root of 625 is 25, for example.

Division Facts beyond the 12 Times Table (Horizontal)

There are certainly a few questions on these worksheets that will be useful knowledge later on. If your students are interested in learning them, anything to do with 16, 20, 24, and 25 will certainly be useful, and likely someone could come up with a reason for learning the others. Sixteen is used in the base 16 (aka hexadecimal system), so converting hexadecimal numbers to decimal numbers involves dividing (and multiplying by 16). Twenty is a great number that is divisible by six different numbers and in turn is a factor of some important numbers. Twenty is also a coin unit in many countries. Twenty-four hours is the length of a day, so if you wanted to know how many days were in 288 hours, you might want to know your 24 times table division facts. Twenty-five, well that is the value of a quarter, isn't it? You could also calculate how many seconds of PAL video you have by dividing the number of frames by 25!

Dividing Individual Facts beyond the 12 Times Table (Vertically)

If the previous two sections are a little tough to handle right out of the gates, perhaps start with these worksheets that only deal with one of the divisors at a time.

Dividing Individual Facts beyond the 12 Times Table (Horizontally)

Even more of the previous section, but with 100 questions per page and a horizonal arrangement.

Long Division Worksheets

Long division worksheets with no remainders.

Need an easier way to divide large numbers? Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder. Example: 1458 ÷ 54. Note 54 × 1 = 54, 54 × 10 = 540 (nothing greater is needed). 1458 - 540 - 540 = 378. Note that 540 was subtracted twice, so the number of times that 54 "goes into" 1458 so far is 20 times. Continuing, 378 - 54 - 54 - 54 - 54 - 54 - 54 - 54 = 0. Since 54 was subtracted seven times, the quotient increases by seven for a total of 27. In other words, 54 "goes into" 1458, 27 times.

We might also mention that this method can be even more sophisticated by using multiples of powers of ten. In the above example, using 54 × 5 = 270 would have helped to get to the quotient quicker.

European Long division worksheets with no remainders

Long division worksheets with remainders

Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders? It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient. For example 19 ÷ 3 is 6 with a remainder of 1 which is more precisely 6 1/3. Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise (e.g. compare 6 1/3 with 6.3333....).

Long division worksheets with decimal quotients

European long division worksheets with remainders

European long division worksheets with decimal quotients

Long Division with Remainders worksheets with the steps shown on the answer key

We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school. Learning this algorithm by itself is sometimes not enough as it may not lead to a good conceptual understanding. One tool that helps students learn the standard algorithm and develop an understanding of division is a set of base ten blocks. By teaching students division with base ten blocks first then progressing to the standard algorithm, students will gain a conceptual understanding plus have the use of an efficient algorithm for long division. Students who have both of these things will naturally experience more success in their future mathematical studies.

Long Division on a Grid

Long division with grid assistance and no remainders worksheets.

Some students find it difficult to get everything lined up when completing a long division algorithm, so these worksheets include a grid and wider spacing of the digits to help students get things in the right place. The answer keys include the typical steps that students would record while completing each problem; however, slight variations in implementation may occur. For example, some people don't bother with the subtraction signs,some might show steps subtracting zero, etc.

Long division with grid assistance and SOME remainders worksheets

Divisibility Rules

Worksheets for practicing divisibility rules including a variety of small and large numbers and focusing on various divisors.

Divisibility rules

Divisibility by 2, 5 and 10

A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2. A number is divisible by 5 if the final digit is a 0 or a 5. A number is divisible by 10 if the final digit is a 0.

Divisibility by 3, 6 and 9

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3. A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules). A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.

Divisibility by 4, 7 and 8

A number is divisible by 4 if the last two digits of the number are divisible by 4. For 7, there are a couple of strategies to use. Please see Divisibility Tricks for Learning Math for more information. A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.

Dividing in Other Base Number Systems

Dividing numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

Dividing in other base number systems

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• Division Worksheets

Help kids learn division with this collection of printable worksheets. These worksheets are perfect for kids that are just starting to learn division and looking for some printable pages of easy problems to solve. All these division worksheets come with answer keys.

Simple Division Worksheet 1

16 simple division problems

Simple Division Worksheet 2

Simple Division Worksheet 3

Simple Division Worksheet 4

Simple Division Worksheet 5

Simple Division Worksheet 6

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Division Word Problem Worksheets

This page contains extensive division word problems replete with engaging scenarios that involve two-digit and three-digit dividends and single digit divisors; three-digit dividends and two-digit divisors; and advanced division worksheets (four-digit and five-digit dividends). Thumb through some of these worksheets for free!

Division Word Problems for Beginners

These printable worksheets feature simple division word problems. The divisors are in the range 2 to 9. The quotients are in the range 2 to 10. These worksheets are building blocks for children.

Division: Two-digit by Single-digit (without Remainder)

This set of word problems involves dividing a two-digit number by a single-digit number to arrive at a quotient. The division leaves no remainder. Answer key is included in each worksheet.

Division: Two-digit by Single-digit (with Remainder)

These word problems require the learner to divide the two-digit dividend by the single-digit divisor and write down both the quotient and the remainder. Three pdf worksheets with 15 scenarios are featured here.

Theme based Word Problems

Each worksheet has five word problems related to the given theme. Supermarket, School and Halloween party are the themes used here.

Three-digit by Single-digit Word Problems

These printable worksheets involve division word problems with three-digit dividends and single digit divisors. Apply long division method to solve each problem.

Three-digit by Two-digit Word Problems

This set of word problems will require the student to perform division operations involving three-digit numbers and two-digit numbers. Verify your answer with the answer key provided in the worksheet.

Division: Four or Five-digit by Single-digit

Interesting scenarios are presented in these advanced worksheet pdfs that involve four-digit and five-digit dividends and single digit divisors. Use long division method to find the quotient.

Related Worksheets

» Addition Word Problems

» Subtraction Word Problems

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Division Worksheets

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Unit 5: Division

About this unit.

• Division: FAQ (Opens a modal)
• Estimating division that results in non-whole numbers (Opens a modal)
• Understanding remainders (Opens a modal)
• Introduction to remainders (Opens a modal)
• Interpreting remainders (Opens a modal)
• Estimate to divide by 1-digit numbers Get 3 of 4 questions to level up!
• Interpret remainders Get 3 of 4 questions to level up!
• Divide with remainders (2-digit by 1-digit) Get 3 of 4 questions to level up!

Divide multiples of 10, 100, and 1,000 by 1-digit numbers

• Quotients that are multiples of 10 (Opens a modal)
• Divide multiples of 10, 100, and 1,000 by 1-digit numbers Get 5 of 7 questions to level up!

Division with place value

• Division using place value (Opens a modal)
• Divide using place value Get 3 of 4 questions to level up!

Division with area models

• Division with area models (Opens a modal)
• Create division equations with area models Get 3 of 4 questions to level up!
• Divide by 1-digit numbers with area models Get 3 of 4 questions to level up!

Estimate quotients

• Estimating quotients (Opens a modal)
• Estimate quotients (3- and 4-digit divided by 1-digit) Get 3 of 4 questions to level up!

Multi-digit division with partial quotients

• Introduction to division with partial quotients (no remainder) (Opens a modal)
• Division with partial quotients (remainder) (Opens a modal)
• Intro to long division (no remainders) (Opens a modal)
• Divide multi-digit numbers by 2, 3, 4, and 5 (remainders) Get 5 of 7 questions to level up!
• Divide multi-digit numbers by 6, 7, 8, and 9 (remainders) Get 3 of 4 questions to level up!

Multiplication, division word problems

• Division word problem: field goals (Opens a modal)
• Multiplication word problem: pizza (Opens a modal)
• Multiplication and division word problems Get 5 of 7 questions to level up!

Multi-step word problems

• 2-step estimation word problem (Opens a modal)
• 2-step estimation word problems Get 3 of 4 questions to level up!
• Represent multi-step word problems using equations Get 3 of 4 questions to level up!
• Multi-step word problems with whole numbers Get 3 of 4 questions to level up!

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Division problems - set up the long division yourself

In these worksheets, the student has to set up the long division himself (the division problem is written horizontally at the top of the workspace).

Long division with two-digit divisor

Three-digit divisors.

The following worksheets are for three-digit divisors. The divisions are exact. If you're looking for division with remainders, you can make worksheets using the generator below or go to this page for some ready-made worksheets.

Division worksheets generator

Use the generator to make customized worksheets, including horizontally written problems, long division, and division with remainders.

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How to Do Long Division

Last Updated: July 29, 2023 References

This article was co-authored by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed 3,689,766 times.

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals . This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life. [1] X Research source

• The quotient (answer) will eventually go on top, right above the dividend.
• Leave yourself plenty of space below the equation to carry out multiple subtraction operations.
• Here's an example: if there are six mushrooms in a 250-gram pack, how much does each mushroom weigh on average? In this case, we must divide 250 by 6. The 6 goes on the outside, and the 250 on the inside.

• In our example, you'd want to determine how many times 6 goes into 2. Since six is larger than two, the answer is zero. If you wish, may write a 0 directly above the 2 as a place-holder, and erase it later. Alternatively, you can leave that space blank and move on to the next step.

• If your answer to the previous step was 0, as in the example, expand the number by one digit. In this case, we'd ask how many times 6 can go into 25.
• If your divisor has more than two digits, you'll have to expand out even further, to the third or maybe even fourth digit of the dividend in order to get a number that the divisor goes into.
• Work in terms of whole numbers . If you use a calculator , you'll discover that 6 goes into 25 a total of 4.167 times. In long division, you always round down to the nearest whole number, so in this case, our answer would be 4.

• It is important in long division to make sure the columns of numbers remain correctly aligned. Work carefully, otherwise you may make an error that leads you to the wrong answer.
• In the example, you would place a 4 above the 5, since we're putting 6 into 25.

Multiplying

• In the example, 6 times 4 is 24. After you've written a 4 in the quotient, write the number 24 beneath the 25, again being careful to keep the numbers aligned.

Subtracting

• In the example, we'll subtract 24 from 25, getting 1.
• Do not subtract from the complete dividend, but only those digits you worked with in Parts One and Two. In the example, you should not subtract 24 from 250.

• In the example, because 6 can't go into 1 without exceeding it, you need to bring down another digit. In this case, you'll grab the 0 from 250 and place it after the 1, making it 10, which 6 can go into.

• In the example, determine how many times 6 can go into 10. Write that number (1) into the quotient above the dividend. Then multiply 6 by 1, and subtract the result from 10. You should end up with 4.
• If your dividend has more than three digits, keep repeating this process until you've worked through all of them. For example, if we we had started with 2,506 grams (88.4 oz) of mushrooms, we'd pull the 6 down next and place it next to the four.

Remainders and Decimals

• In the example, the remainder would be 4, because 6 cannot go into four, and there are no more digits to bring down.
• Place your remainder after the quotient with a letter "r" before it. In the example, the answer would be expressed as "41 r4."
• You would stop here if you were trying to calculate something that would not make sense to express in partial units , for example, if you were trying to determine how many cars were needed to move a certain number of people. In a case such as this, it would not be useful think about things in terms of partial cars or partial people.
• If you plan to calculate a decimal, you can skip this step.

• In the example, since 250 is a whole number, every digit after the decimal will be 0, making it 250.000.

• In the example, determine how many times 6 can go into 40. Add that number (6) to the quotient above the dividend and after the decimal point. Then multiply 6 by 6, and subtract the result from 40. You should end up with 4 again.

• In the example, you could keep getting 4 out of 40-36 forever, and add 6's to your quotient indefinitely. Instead of doing this, stop the problem and round the quotient. Because 6 is greater than (or equal to) 5, you would round up to 41.67.
• Alternatively, you can indicate a repeating decimal by placing a small horizontal line over the repeating digit. In the example, this would make the quotient 41.6, with a line over the 6. [15] X Research source

• If you added a zero as a place-holder at the beginning, you should erase that now as well.
• In the example, because you asked how much each mushroom in a 250-gram pack of 6 weighs, you'll need to put your answer into grams. Therefore, your final answer is 41.67 grams.

Practice Problems and Answers

Community Q&A

Video . By using this service, some information may be shared with YouTube.

• If you have time, it's a good idea to do calculations on paper first, then check with a calculator or computer. Remember that machines sometimes get the answers wrong for various reasons. If there is an error, you can do a third check using logarithms . Doing division by hand rather than relying on machines is good for your mathematical skills and conceptual understanding. [16] X Research source Thanks Helpful 0 Not Helpful 0
• Start by using simple calculations. This will give you the confidence and develop the necessary skills to move to more advanced ones. Thanks Helpful 7 Not Helpful 7
• Look for practical examples from everyday life. This will help learn the process because you can see how it is useful in the real world. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ https://www.csun.edu/~vcmth00m/longdivision.pdf
• ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut36_longdiv.htm
• ↑ https://www.calculatorsoup.com/calculators/math/longdivision.php
• ↑ https://www.mathsisfun.com/long_division.html
• ↑ https://www.bbc.co.uk/bitesize/guides/z3kmpbk/revision/4
• ↑ https://flexbooks.ck12.org/cbook/ck-12-fifth-grade-math-resource-flexlet/section/1.1/primary/lesson/long-division-without-remainders/
• ↑ https://www.mathsisfun.com/long_division2.html
• ↑ https://www.calculatorsoup.com/calculators/math/longdivisiondecimals.php
• ↑ https://www.mathsisfun.com/definitions/recurring-decimal.html

About This Article

To do long division, follow these seven steps: Step 1. Calculate how many times the number outside the division bar goes into the first number inside the bar. Step 2. Put the answer on top of the bar. Step 3. Multiply the number outside the division bar by the number at the top of the bar. Step 4. Write the answer below the number inside the division bar, so the first digits of both numbers are lined up. Step 5. Subtract the two numbers inside the division bar and write the answer below the two numbers. If there are any remaining digits inside the division bar, bring them down to the new answer. Step 6. Repeat the division process with the new number. Step 7: If you get to a point where the number outside the division bar can’t fit into the remaining number, write that number, also known as the remainder, next to your answer with an “r” in front of it. Did this summary help you? Yes No

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Biden’s New Student Loan Repayment Plan Is Open. Here’s How to Enroll.

The income-driven plan, SAVE, will reduce payments for millions of borrowers, and more will qualify for $0 payments.

By Tara Siegel Bernard

Borrowers who are buckling under the pressure of their federal student loans have a new option to significantly cut their payments, eventually by as much as half.

The Biden administration’s new income-driven repayment plan, known as SAVE, opened for enrollment on Tuesday, providing millions of borrowers with a more affordable way to pay their monthly student loan bills, which will become due again in October after a three-year pause.

“With the SAVE plan, we are making a promise to every student,” Education Secretary Miguel Cardona said during a call with reporters on Monday afternoon. “Your payments will be affordable. You’re not going to be buried under a mountain of interest, and you won’t be saddled with a lifetime of debt.”

In the coming days, more than 30 million borrowers will be invited to enroll in the plan, which was initially proposed in January and bases monthly payments on income and family size.

Unlike the White House’s former plan to cancel up to $20,000 in federal debt — struck down by the Supreme Court in June — this payment option will become a permanent piece of the student loan machinery and be available to current and future borrowers. It also creates a new safety net, automatically enrolling certain borrowers into the SAVE plan after they have fallen behind on their payments.

Borrowers who want to sign up for the SAVE — or Saving on a Valuable Education — plan should move quickly: You can expect to wait roughly four weeks for your application to be processed, senior Education Department officials said. By enrolling now, you can have your paperwork processed with enough time before your first payment becomes due, officials added.

Borrowers won’t receive the full benefits of the plan until next summer, because some features won’t immediately take effect. Here’s a rundown on how the plan will work:

Who is eligible for the new repayment plan?

Those with federal undergraduate or graduate loans. Borrowers with undergraduate debt are eligible for lower payments than graduate borrowers.

Who is excluded?

Parents who borrowed to pay for their children’s schooling using Parent PLUS loans cannot enroll in the new plan.

If parent borrowers cannot afford to make their payments, they generally have access to only the most expensive income-driven repayment plan — known as income-contingent repayment — which requires borrowers to pay 20 percent of their discretionary income for 25 years; anything remaining is forgiven.

How does the new SAVE plan work?

All income-driven repayment plans generally operate the same way. Payments are based on your earnings and household size, and are readjusted each year. After monthly payments are made for a set number of years, usually 20, any remaining balance is forgiven. (The balance is taxable as income, though a temporary tax rule exempts balances forgiven through 2025 from federal income taxes.)

The SAVE plan — which replaced the Revised Pay as You Earn program, or REPAYE — is more generous in several ways. To start, it would reduce payments on undergraduate loans to 5 percent of discretionary income, down from 10 percent in REPAYE (and 15 percent in other plans).

Graduate debt is also eligible, but borrowers would pay 10 percent of discretionary income on that portion. If you hold both undergraduate and graduate debt, your payment will be weighted accordingly.

The new rules also tweak the payment formula by protecting more income for basic needs, which in turn reduces payments overall. That change will also allow more low-income workers to qualify for $0 payments.

What is discretionary income?

Once you pay for basic needs like food and rent, any leftover income is considered discretionary; income-driven repayment plans require borrowers to pay a percentage of that discretionary income.

The SAVE plan tweaks the payment formula so that more income is shielded for those basic needs, generating less discretionary income and a lower payment.

SAVE increases the amount of income protected from repayment to 225 percent of the federal poverty guidelines, roughly equivalent to $15 an hour for a single borrower. If you earn less than that, you won’t have to make a monthly payment.

Put another way, a single person who makes less than $32,805 a year would make $0 monthly payments. The same goes for someone in a household of four with income below $67,500. That should help an additional one million low-income borrowers qualify for a zero-dollar payment, the Education Department said.

Under the old REPAYE program, less income was shielded, or up to 150 percent of the federal poverty guidelines.

Will the way interest is treated change?

Yes. This is one of the most attractive features of the new plan. If a borrower’s monthly payment does not cover the interest owed, the Education Department will cancel the uncovered portion.

In other words, if a borrower owes $50 in interest each month but the payment covers only $30, the remaining $20 will disappear as long as the payment is made. And monthly interest will be canceled for those who are not required to make payments because their income is too low.

This new rule will provide relief to those who made payments but saw their balances balloon because they didn’t pay enough to cover the interest owed.

Does the plan go into effect right away?

Three big components of the plan are available now, including shielding more income from the repayment formula, which will reduce more borrowers’ payments to zero. The new treatment of unpaid interest is also in effect. Lastly, married borrowers who file their taxes separately will no longer be required to include their spouse’s income in their monthly payment calculation. (They will also have their spouse excluded from their family size.)

But other benefits — including cutting payments to 5 percent from 10 percent of discretionary income on undergraduate loans — won’t take effect until July.

Once the plan is in full swing next summer, many borrowers’ monthly bills, per dollar, will drop 40 percent compared with the REPAYE plan. But the lowest earners may see their payments fall 83 percent, while the highest earners would receive only a 5 percent reduction.

Are there any changes for borrowers with small loan balances?

Yes, but this feature takes effect next summer.

People who took out smaller loans — or those with original balances of $12,000 or less — would make monthly payments for 10 years before cancellation, instead of the more typical 20-year repayment period in other income-driven repayment plans. Every $1,000 borrowed above the $12,000 amount would add one year of monthly payments before the balance was forgiven, up to a maximum of 20 or 25 years.

Will the new plan always be the best option?

The SAVE plan is expected to provide the lowest payment for most borrowers and will probably be the best option for most. The loan simulator tool at StudentAid.gov can help you analyze which repayment plan makes the most sense given your circumstances and goals.

When you sign in, it should automatically use your loans in its calculations. (You can add other federal loans if any are missing.) You can also compare plans side by side — how much they’ll cost over time, both monthly and in total, and if any debt would be forgiven.

What about borrowers who were in default before payments were paused?

Borrowers who fell into default before the payment pause — which happens when you’re at least 270 days behind — have received a fresh start and are considered current on their payments. That means they can enroll in SAVE or any other repayment plan.

But they need to take certain steps to do so — and complete them before September 2024 to keep their loans out of default for the long term.

Here’s how: Contact the Education Department’s Default Resolution Group — by phone, online or mail — and ask to take your loans out of default through the “Fresh Start” program. The default group can also help you enroll in an income-driven repayment plan, including SAVE.

The group will transfer your loans to a regular loan servicer and wipe the record of default from your credit report.

“Their new servicer will then put them into the I.D.R. plan with the lowest monthly payment they are eligible for,” a spokesman for the Education Department said. “For most borrowers, this is SAVE.”

Can delinquent borrowers enroll?

Borrowers who fell behind on their monthly student loan bills before the payment pause have also received a fresh start and will be permitted to enroll in the SAVE program, just like any other borrower.

Going forward, borrowers who go 75 days without making a payment will be automatically enrolled in the SAVE plan — as long as they have provided approval to disclose their federal tax information to the Education Department. This policy will take effect next July.

How do I sign up?

You can sign up online at StudentAid.gov/SAVE ; borrowers will be able to see their payment amount before signing up. Administration officials said the process shouldn’t take more than 10 minutes. After applying, you can check the status of your application by visiting your account dashboard.

And for the next few months, loan servicers will also be able to help borrowers enroll and “self-certify” their income without needing tax documentation, either through the servicer’s website or over the phone, said Scott Buchanan, the executive director of Student Loan Servicing Alliance , an industry trade group.

Those who were already enrolled in REPAYE don’t have to do anything — they will be automatically transferred into SAVE, and their payment amounts will be adjusted. It’s also possible to switch from another income-driven repayment plan into SAVE, without resetting the clock on your payments.

For more information about the repayment start, here is our guide.

What happens if I try to enroll, but my application cannot be processed in time for my first payment?

You will be placed in forbearance, meaning no payment will be due, for the next billing cycle.

Do I have to do anything to remain enrolled?

Your payment size adjusts each year based on your earnings, and your income needs to be updated annually.

But if you give the Education Department permission to access your income information through the Internal Revenue Service (something you can do now during the sign-up process), you will not need to recertify your income each year because it will be done automatically.

Tara Siegel Bernard covers personal finance. Before joining The Times in 2008, she was deputy managing editor at FiLife, a personal finance website, and an editor at CNBC. She also worked at Dow Jones and contributed regularly to The Wall Street Journal. More about Tara Siegel Bernard

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