How To Do Long Division, Step By Step
The short version
- Long division repeats four steps: divide, multiply, subtract, bring down. Repeat until there are no digits left to bring down.
- Whatever is left at the end is the remainder. Write it as R5, as a fraction over the divisor, or keep going with a decimal point.
- Always check by multiplying: quotient × divisor + remainder should equal the number you started with.
- Two digit divisors use the same four steps. The only new skill is estimating, and you’re allowed to guess and adjust.
- Most long division trouble is really multiplication fact trouble. Watch which step your child stalls on.
Long division is the written method for dividing big numbers by hand, and it runs on a four step loop: divide, multiply, subtract, bring down. Set the problem up with the dividend under the bracket and the divisor outside, then work left to right through the dividend one digit at a time. When you run out of digits, you’re done, and anything left over is the remainder.
That’s the whole procedure. What follows is every piece worked out with real numbers, including the two digit divisors most explanations skip, plus the mistakes that cause almost all wrong answers.
The vocabulary first
Teachers use these words constantly, and a kid who doesn’t know them can’t follow instructions.
| Word | Where it sits | In 936 ÷ 4 = 234 |
|---|---|---|
| Dividend | Inside the bracket | 936 |
| Divisor | Outside, to the left | 4 |
| Quotient | On top of the bracket | 234 |
| Remainder | Left over at the end | 0 |
The four steps
Divide. How many times does the divisor go into the digits you’re looking at? Write that on top, lined up over the digit you stopped at.
Multiply. Multiply that quotient digit by the divisor and write the result underneath.
Subtract. Subtract. What’s left must be smaller than the divisor. If it isn’t, your quotient digit was too small.
Bring down. Bring the next digit of the dividend down next to the difference. Start over.
Worked example: 936 ÷ 4
Divide: 4 goes into 9 two times. Write 2 above the 9.
Multiply: 4 × 2 = 8. Write 8 under the 9.
Subtract: 9 – 8 = 1.
Bring down: bring down the 3 to make 13.
Divide: 4 goes into 13 three times. Write 3 above the 3.
Multiply: 4 × 3 = 12. Subtract: 13 – 12 = 1.
Bring down: bring down the 6 to make 16.
Divide: 4 goes into 16 four times. Write 4 above the 6.
Multiply: 4 × 4 = 16. Subtract: 16 – 16 = 0.
Nothing left to bring down. Answer: 234
Check it: 234 × 4 = 936. Correct.
What to do with a remainder
Worked example: 587 ÷ 6
6 doesn’t go into 5, so take the first two digits instead and look at 58.
Divide: 6 goes into 58 nine times. Write 9 above the 8.
Multiply: 6 × 9 = 54. Subtract: 58 – 54 = 4.
Bring down: bring down the 7 to make 47.
Divide: 6 goes into 47 seven times. Write 7 above the 7.
Multiply: 6 × 7 = 42. Subtract: 47 – 42 = 5.
No digits left, and 5 is smaller than 6, so 5 is the remainder.
Answer: 97 R5
Check it: 97 × 6 = 582, and 582 + 5 = 587. Correct.
You can write that remainder three ways, and which one you use depends on the question.
| Form | Looks like | Use it when |
|---|---|---|
| Remainder | 97 R5 | Counting whole things, like buses or boxes |
| Fraction | 97 and 5/6 | The quantity can be split, like pizza or rope |
| Decimal | 97.8333… | Money, measurement, or a calculator answer |
Long division with two digit divisors
This is where most kids give up, and it’s usually because nobody told them that estimating is allowed. You are supposed to guess, check, and fix.
Worked example: 1,248 ÷ 24
24 doesn’t fit into 1 or into 12, so start with 124.
Estimate: 24 × 5 = 120, and 24 × 6 = 144, which is too big. So the digit is 5.
Write 5 above the 4 of 124. Multiply: 24 × 5 = 120. Subtract: 124 – 120 = 4.
Bring down the 8 to make 48.
Divide: 24 × 2 = 48 exactly. Write 2. Subtract: 48 – 48 = 0.
Answer: 52
Check it: 52 × 24 = 1,248. Correct.
Worked example: 945 ÷ 15
15 doesn’t go into 9, so look at 94.
Estimate: 15 × 6 = 90, and 15 × 7 = 105, which is too big. So the digit is 6.
Write 6 above the 4. Subtract: 94 – 90 = 4. Bring down the 5 to make 45.
Divide: 15 × 3 = 45 exactly. Write 3. Subtract: 45 – 45 = 0.
Answer: 63
The useful habit here is writing a short multiplication list in the margin before starting: 15, 30, 45, 60, 75, 90. With that list sitting there, every estimate becomes a lookup instead of a guess. This one trick turns two digit divisors from impossible into routine.
When the answer keeps going: decimals in brief
If you want a decimal instead of a remainder, put a decimal point in the quotient directly above the one in the dividend, add zeros after it, and keep looping.
7 ÷ 8: 8 doesn’t go into 7, so write 0, add a decimal point and a zero to make 70.
8 goes into 70 eight times. 8 × 8 = 64. Subtract: 70 – 64 = 6. Bring down a zero to make 60.
8 goes into 60 seven times. 8 × 7 = 56. Subtract: 60 – 56 = 4. Bring down a zero to make 40.
8 goes into 40 five times exactly. Answer: 0.875
Common mistakes in long division
Digits out of line. Every quotient digit sits above the dividend digit you just used. When the columns drift, answers come out ten times too big or too small. Graph paper fixes this in a week.
Forgetting the zero in the quotient. In 2,408 ÷ 8, after the first step 8 doesn’t go into 0, so a 0 belongs in the quotient before you move on. Skip it and 301 turns into 31.
A remainder bigger than the divisor. If you subtract and get a number as big as the divisor, the quotient digit was too small. Bump it up by one and redo that step.
Guessing too high with two digit divisors. If the subtraction goes negative, back the digit down. Erasing and retrying is normal, not failure.
Never checking. Multiply the quotient by the divisor and add the remainder. It takes ten seconds and catches nearly everything.
Practice problems
1. 84 ÷ 4
2. 276 ÷ 6
3. 435 ÷ 5
4. 731 ÷ 7
5. 2,408 ÷ 8
6. 672 ÷ 21
7. 1,035 ÷ 23
8. 5,684 ÷ 12
Answers
1. 21. Check: 21 × 4 = 84.
2. 46. Check: 46 × 6 = 276.
3. 87. Check: 87 × 5 = 435.
4. 104 R3. Watch the middle step: 7 doesn’t go into 3, so a 0 goes in the quotient. Check: 104 × 7 = 728, and 728 + 3 = 731.
5. 301. Same zero trap. Check: 301 × 8 = 2,408.
6. 32. Estimate with 21 × 3 = 63. Check: 32 × 21 = 672.
7. 45. Estimate with 23 × 4 = 92. Check: 45 × 23 = 1,035.
8. 473 R8. Check: 473 × 12 = 5,676, and 5,676 + 8 = 5,684.
What it means if your child is stuck here
Long division is where hidden gaps surface, because it stacks four skills into one problem. Watch which step breaks and you’ll know what to fix.
Stalling on the divide step usually means multiplication facts aren’t automatic. A kid who has to work out 6 × 7 in the middle of a division problem loses the thread. Errors on the subtract step point at regrouping, a second or third grade skill. Messy columns and misplaced digits point at place value. And a kid who does every step right but can’t tell you what the answer means never had division explained as sharing or grouping in the first place.
Math skills by grade level for grades 3 to 5 shows where division is supposed to land, and 12 signs your child is behind in math by grade level helps you tell a rough week from a real gap. Long division is also a common trigger for tears at the kitchen table, so if your child shuts down before they even pick up the pencil, math anxiety in children is worth reading. And the shaky division of today becomes the shaky rational expressions of algebra, which is the pattern in why algebra trouble usually traces back to fourth grade fractions.
Frequently asked questions
What are the steps of long division in order?
Divide, multiply, subtract, bring down, then repeat. Stop when there are no digits left to bring down. Whatever remains after the last subtraction is the remainder.
What grade is long division taught?
Single digit divisors usually come in fourth grade, and two digit divisors in fifth or sixth, depending on the curriculum.
How do you do long division with two digit numbers?
Exactly the same four steps. Before you start, write out a few multiples of the divisor in the margin, then use that list to pick each quotient digit. If a guess is too big, lower it and redo the step.
What do you do when the divisor doesn’t go into the first digit?
Take one more digit. For 587 ÷ 6, since 6 won’t go into 5, start with 58. If you’re writing a placeholder, put a 0 above that first digit rather than leaving it blank.
How do you check a long division answer?
Multiply the quotient by the divisor, then add the remainder. You should get the dividend back. For 97 R5 with a divisor of 6: 97 × 6 = 582, plus 5, gives 587.
Is long division still worth learning?
Yes. Beyond the arithmetic, the same procedure returns in algebra for dividing polynomials, and the estimate and adjust habit it builds shows up all over higher math.
Find the actual gap
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