When Is Long Division Taught? A Grade-by-Grade Math Guide
Long division starts in 4th grade, moves to two-digit divisors in 5th and is expected to be fluent by 6th. What each grade learns, with Common Core standards.
Long division is one of the most important math skills your child will learn — but when exactly do they learn it? Many parents are surprised to find that long division isn't taught all at once. It's introduced gradually, building on skills learned in earlier grades.
If you've ever wondered "When is long division taught?" or "What grade do kids learn long division?" — this guide is for you. We'll walk you through the grade-by-grade progression so you know exactly what to expect at each stage. The grade levels below follow the Common Core State Standards, which most US states use or have adapted; a few states, such as Texas, write their own standards, so the timing in your child's school can differ by a year.
In this guide, you'll learn:
- When long division is taught — a grade-by-grade timeline
- What 3rd graders learn — the basics of division
- What 4th graders learn — the introduction to long division
- What 5th graders learn — two-digit divisors and decimals
- What 6th graders and beyond learn — the standard algorithm, fractions, decimals and algebra
- How to help your child at each grade — parent tips
- Practice problems with answers
- Common mistakes and how to help
- FAQs — common parent questions
Let's dive in and understand the long division journey!
Quick Answer
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| Grade | Age | What Students Learn |
|---|---|---|
| 3rd Grade | 8-9 | Basic division concepts (equal groups, arrays, division facts within 100) |
| 4th Grade | 9-10 | Introduction to long division (one-digit divisors, up to four-digit dividends) |
| 5th Grade | 10-11 | Two-digit divisors, and dividing decimals to hundredths |
| 6th Grade | 11-12 | Fluency with the standard long division algorithm, multi-digit decimals, dividing fractions |
| 7th-8th Grade | 12-14 | Using long division to turn fractions into decimals, including repeating decimals |
| High School | 14-18 | Polynomial long division (usually Algebra 2) |
3rd Grade: The Basics of Division
In 3rd grade, students are introduced to division concepts — but not formal long division.
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| Concept | What It Means | Example |
|---|---|---|
| Equal Groups | Dividing objects into equal groups | 12 ÷ 3 = 4 groups of 3 |
| Arrays | Arranging objects in rows and columns | 12 objects in 3 rows of 4 |
| Repeated Subtraction | Subtracting the same number repeatedly | 12 − 3 − 3 − 3 − 3 = 0 (4 times) |
| Multiplication Facts | Using times tables to divide | 12 ÷ 3 = 4 because 3 × 4 = 12 |
| Simple Division Facts | Dividing within 100 | 20 ÷ 5 = 4 |
Common Core standard 3.OA.A.2 asks students to interpret whole-number quotients as shares or groups, and 3.OA.C.7 asks them to multiply and divide fluently within 100 and, by the end of 3rd grade, know all products of two one-digit numbers from memory. That last part matters more than anything else for long division the following year.
What 3rd graders do NOT learn
- The long division algorithm
- Multi-digit divisors
- Remainders in long division format
Parent tips for 3rd grade
- Practice multiplication facts daily
- Use real objects (blocks, candy) to show division
- Play division games
- Don't rush to long division — build the foundation first
4th Grade: Introduction to Long Division
In 4th grade, students are formally introduced to long division.
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| Concept | What It Means | Example |
|---|---|---|
| Long Division Setup | Dividend, divisor, quotient | 4 ) 48 |
| 1-Digit Divisors | Dividing by numbers 2-9 | 48 ÷ 4 = 12 |
| Basic Remainders | Leftover numbers | 47 ÷ 4 = 11 R3 |
| Visual Methods | Partial quotients, area model | Breaking problems into chunks |
| Place Value | Understanding thousands, hundreds, tens, ones | 456 ÷ 3 = 152 |
What 4th graders do NOT learn
- 2-digit divisors
- Dividing decimals
- Complex multi-step problems
Parent tips for 4th grade
- Use the DMSBR acronym (Divide, Multiply, Subtract, Bring Down, Repeat). The long division cheat sheet for parents turns it into the "Dad, Mom, Sister, Brother, Rover" memory trick
- Use graph paper to keep numbers aligned
- Practice with simple problems first
- Check work using multiplication
5th Grade: Two-Digit Divisors
In 5th grade, students extend long division to two-digit divisors and begin dividing decimals.
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| Concept | What It Means | Example |
|---|---|---|
| 2-Digit Divisors | Dividing by numbers 10-99 | 144 ÷ 12 = 12 |
| Larger Dividends | Up to four-digit dividends | 5,432 ÷ 8 = 679 |
| Estimation | Rounding to predict the answer | 3,456 ÷ 24 is about 3,500 ÷ 25 = 140 |
| Decimals to Hundredths | Dividing simple decimals | 7.2 ÷ 0.8 = 9 |
| Word Problems | Real-world division problems | Sharing, grouping |
Parent tips for 5th grade
- Practice 2-digit divisors regularly; the guide to 2-digit, 3-digit and decimal divisors has worked examples
- Use estimation to check answers
- Show the connection to fractions
- Use a calculator to verify answers
6th Grade and Beyond: Fluency, Decimals and Algebra
In 6th grade, Common Core standard 6.NS.B.2 expects students to "fluently divide multi-digit numbers using the standard algorithm", and 6.NS.B.3 extends that to multi-digit decimals. This is the grade where the written long division method is expected to be quick and accurate.
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| Concept | What It Means | Example |
|---|---|---|
| Standard Algorithm Fluency | Speed and accuracy with the written method | 5,544 ÷ 63 = 88 |
| Multi-Digit Decimals | Dividing decimals by decimals | 12.5 ÷ 0.5 = 25 |
| Dividing Fractions | Fractions divided by fractions (6.NS.A.1) | (2/3) ÷ (3/4) = 8/9 |
| Ratio and Rate | Using division in real-life contexts | Speed, unit price |
Dividing fractions uses the same "how many groups" idea as whole numbers; the fraction operations guide shows the multiply-by-the-reciprocal method step by step.
What 7th-8th graders learn
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| Grade | Concept | Example |
|---|---|---|
| 7th (7.NS.A.2d) | Convert a fraction to a decimal using long division | 3/8 = 0.375; 2/3 = 0.666… |
| 7th | Know that the decimal either ends or eventually repeats | 1/7 = 0.142857142857… |
| 8th (8.NS.A.1) | Convert a repeating decimal back into a fraction | 0.333… = 1/3 |
To see the decimal for any fraction, and whether it repeats, the fraction to decimal calculator does the long division for you.
What high school students learn
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| Concept | What It Means | Example |
|---|---|---|
| Polynomial Long Division | Dividing algebraic expressions (HSA-APR.D.6) | (x² + 3x + 2) ÷ (x + 1) = x + 2 |
| Synthetic Division | A shortcut for dividing by (x − a), taught in many Algebra 2 and precalculus courses | Finding roots of polynomials |
| Rational Expressions | Writing a(x)/b(x) as q(x) + r(x)/b(x) | Simplifying algebraic fractions |
Parent tips for 6th grade and beyond
- Connect division to fractions and decimals
- Practice with real-world problems
- Introduce algebraic thinking
- Use a calculator for complex problems
Grade-by-Grade Summary Table
Here's a complete overview of when long division is taught:
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| Grade | Age | Long Division Focus | Key Skills |
|---|---|---|---|
| 3rd | 8-9 | Division basics | Equal groups, arrays, multiplication facts |
| 4th | 9-10 | Introduction | 1-digit divisors, basic remainders |
| 5th | 10-11 | Two-digit divisors | 2-digit divisors, decimals to hundredths |
| 6th | 11-12 | Fluency | Standard algorithm, multi-digit decimals, fraction division |
| 7th-8th | 12-14 | Fractions to decimals | Terminating and repeating decimals |
| High school | 14-18 | Algebra | Polynomial long division |
How Long Division Fits into the Curriculum
Long division is part of the Common Core State Standards for mathematics.
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| Grade | Standard | What It Says |
|---|---|---|
| 3rd | 3.OA.A.2 | Interpret whole-number quotients of whole numbers |
| 3rd | 3.OA.C.7 | Fluently multiply and divide within 100 |
| 4th | 4.NBT.B.6 | Find quotients and remainders with up to four-digit dividends and one-digit divisors |
| 5th | 5.NBT.B.6 | Find quotients with up to four-digit dividends and two-digit divisors |
| 5th | 5.NBT.B.7 | Divide decimals to hundredths |
| 6th | 6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm |
| 6th | 6.NS.B.3 | Fluently divide multi-digit decimals using the standard algorithm |
| 7th | 7.NS.A.2d | Convert a rational number to a decimal using long division |
| High school | HSA-APR.D.6 | Rewrite rational expressions using inspection or long division |
Why this progression matters
- Each grade builds on the last
- Students need time to master each step
- Rushing causes gaps in understanding
What Parents Can Expect at Each Grade
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| Grade | What Your Child Should Be Able To Do |
|---|---|
| 3rd | Understand division as sharing or grouping, and know division facts within 100 |
| 4th | Divide 2-4 digit numbers by 1-digit numbers, with remainders |
| 5th | Divide by 2-digit numbers, and divide simple decimals |
| 6th | Use the standard algorithm fluently, including with decimals |
| 7th-8th | Turn fractions into decimals and repeating decimals into fractions |
| High school | Divide polynomials in algebra |
If your child is struggling
- Review previous grade skills
- Practice multiplication facts
- Use visual aids
- Be patient and encouraging
Practice Problems (With Answers)
Problem 1 (4th grade level): 48 ÷ 4 = ?
- 4 goes into 4 once → write 1
- 1 × 4 = 4, 4 − 4 = 0
- Bring down 8
- 4 goes into 8 twice → write 2
- 2 × 4 = 8, 8 − 8 = 0
- Answer: 12
Problem 2 (4th grade level): 147 ÷ 7 = ?
- 7 does not fit into 1
- 7 fits into 14 twice → write 2
- 2 × 7 = 14, 14 − 14 = 0
- Bring down 7
- 7 fits into 7 once → write 1
- Answer: 21
Problem 3 (5th grade level): 1,248 ÷ 12 = ?
- 12 fits into 12 once → write 1
- 1 × 12 = 12, 12 − 12 = 0
- Bring down 4
- 12 does not fit into 4 → write 0
- Bring down 8, giving 48
- 12 fits into 48 four times → write 4
- 4 × 12 = 48, 48 − 48 = 0
- Answer: 104
Problem 4 (5th grade level): 3,456 ÷ 24 = ?
- 24 does not fit into 3, so look at 34
- 24 fits into 34 once → write 1
- 1 × 24 = 24, 34 − 24 = 10
- Bring down 5, giving 105
- 24 fits into 105 four times → write 4
- 4 × 24 = 96, 105 − 96 = 9
- Bring down 6, giving 96
- 24 fits into 96 four times → write 4
- 4 × 24 = 96, 96 − 96 = 0
- Answer: 144
Problem 5 (6th grade level): 15.5 ÷ 2.5 = ?
- Move both decimal points one place right: 155 ÷ 25
- 25 fits into 155 six times → write 6
- 6 × 25 = 150, 155 − 150 = 5
- Add a decimal point and a zero: 50
- 25 fits into 50 twice → write 2
- Answer: 6.2
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| Problem | Grade Level | Answer |
|---|---|---|
| 1 | 4th | 12 |
| 2 | 4th | 21 |
| 3 | 5th | 104 |
| 4 | 5th | 144 |
| 5 | 6th | 6.2 |
The Long Division Calculator shows each of these worked out step by step, which makes it easy to find the exact line where a child's working went wrong.
Common Mistakes at Each Grade Level
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| Grade | Common Mistake | How to Help |
|---|---|---|
| 3rd | Confusing division with subtraction | Use real objects to show grouping |
| 4th | Forgetting to bring down digits | Use DMSBR reminder |
| 4th | Misaligning numbers | Use graph paper |
| 5th | Struggling with 2-digit divisors | Practice estimation first |
| 5th | Forgetting decimal placement | Review place value |
| 6th | Misinterpreting remainders | Practice word problems |
| 7th-8th | Stopping a repeating decimal too early | Watch for a remainder that comes back |
| High school | Skipping missing powers of x in polynomial division | Write 0 placeholders, such as x³ + 0x² + 0x − 8 |
How to Help Your Child at Each Grade
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| Grade | What You Can Do |
|---|---|
| 3rd | Practice multiplication facts, use objects to show division |
| 4th | Teach the DMSBR method, use graph paper |
| 5th | Practice 2-digit divisors, use estimation |
| 6th | Connect division to decimals and fractions |
| 7th-8th | Practice turning fractions into decimals |
| High school | Support algebra learning, use online resources |
General tips for all grades
- Be patient — long division takes time
- Practice regularly (10-15 minutes daily)
- Use real-world examples
- Celebrate small wins
- Use a calculator to check work
Frequently Asked Questions
What grade is long division taught?
Long division is introduced in 4th grade with one-digit divisors, extended to two-digit divisors in 5th grade, and expected to be fluent by the end of 6th grade under the Common Core standards.
When do students learn long division?
Students are introduced to long division in 4th grade (ages 9-10).
What grade is long division taught in Common Core?
4th grade standard 4.NBT.B.6 introduces it with one-digit divisors, 5th grade standard 5.NBT.B.6 adds two-digit divisors, and 6th grade standard 6.NS.B.2 expects fluency with the standard algorithm.
Do 3rd graders learn long division?
No. 3rd graders learn division basics (equal groups, arrays, facts within 100) but not the long division algorithm.
Do 4th graders learn long division?
Yes. 4th graders are introduced to long division with one-digit divisors, often starting with partial quotients or area models.
Do 5th graders learn long division?
Yes. 5th graders divide by two-digit numbers and begin dividing decimals to hundredths.
What grade is polynomial long division taught?
Polynomial long division is a high school algebra topic (Common Core standard HSA-APR.D.6), usually taught in Algebra 2.
How long does it take to learn long division?
Long division is a multi-year skill: introduced in 4th grade, extended in 5th, and fluent by the end of 6th grade.
Is long division still taught in schools?
Yes. Long division is part of the Common Core State Standards; 6.NS.B.2 names the standard algorithm directly.
What if my child is struggling with long division?
Review previous grade skills, practice multiplication facts, use visual aids, and be patient.
Sources
- Common Core State Standards for Mathematics, Grade 3 Operations and Algebraic Thinking (3.OA.A.2, 3.OA.C.7): https://www.thecorestandards.org/Math/Content/3/OA/
- Grade 4 and Grade 5 Number and Operations in Base Ten (4.NBT.B.6, 5.NBT.B.6, 5.NBT.B.7): https://www.thecorestandards.org/Math/Content/4/NBT/ and https://www.thecorestandards.org/Math/Content/5/NBT/
- Grade 6 and Grade 7 The Number System (6.NS.A.1, 6.NS.B.2, 6.NS.B.3, 7.NS.A.2d): https://www.thecorestandards.org/Math/Content/6/NS/ and https://www.thecorestandards.org/Math/Content/7/NS/
- High School Algebra, Arithmetic with Polynomials and Rational Expressions (HSA-APR.D.6): https://www.thecorestandards.org/Math/Content/HSA/APR/
- Standards text read on 2 October 2026. Every practice answer in this guide was recalculated before publishing.
Final Summary
Long division is a multi-year journey that starts in 3rd grade with division basics, formally begins in 4th grade, moves to two-digit divisors in 5th grade, becomes fluent in 6th grade, and returns in 7th grade for decimals and in high school algebra for polynomials.
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| Grade | Focus |
|---|---|
| 3rd | Division basics (equal groups, arrays) |
| 4th | Introduction to long division (1-digit divisors) |
| 5th | Two-digit divisors and simple decimals |
| 6th | Standard algorithm fluency, decimals and fractions |
| 7th-8th | Fractions to decimals |
| High school | Polynomial long division |
Long division builds on previous skills, and each grade adds a new layer. Start practicing now: the Long Division Calculator checks any problem and shows every step.
Written by
Do The Calculation Team
Do The Calculation
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