Division as repeated subtraction

Take the same number away again and again until nothing is left. Count how many times: that is the answer to the division.

The idea: take away equal groups

How many 5s are in 20? Take 5 away from 20, then another 5, and keep going: 20, 15, 10, 5, 0. You took 5 away four times, so 20 ÷ 5 = 4.

This is the grouping side of division. It matches what children do with real objects: “put the sweets in bags of 5” means taking 5 away again and again. Counting the bags gives the answer.

Repeated subtraction is also the mirror of multiplication as repeated addition. 5 + 5 + 5 + 5 = 20 builds up to 20. 20 − 5 − 5 − 5 − 5 = 0 breaks it back down.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

20−5115−5210−535−5405 taken away 4 times: 20 ÷ 5 = 4
20 − 5 − 5 − 5 − 5 = 0: four subtractions, so 20 ÷ 5 = 4.
18−6112−626−6306 taken away 3 times: 18 ÷ 6 = 3
18 take away 6 three times reaches 0: 18 ÷ 6 = 3.
496chunks− 804 × 2016− 164 × 4020 + 4 = 24
Bigger chunks: take away 40 twice and 16 once, then add 10 + 10 + 4 = 24.

How to divide by repeated subtraction

  1. Write the number you are dividing (the dividend).
  2. Take away the divisor and write what is left.
  3. Keep taking away the divisor, making a tally mark each time.
  4. Stop when you reach 0, or when what is left is smaller than the divisor.
  5. Count the tally marks. That is the quotient. Anything left over is the remainder.

Example: 18 ÷ 3. 18 − 3 = 15, 15 − 3 = 12, 12 − 3 = 9, 9 − 3 = 6, 6 − 3 = 3, 3 − 3 = 0. Six tally marks, so 18 ÷ 3 = 6.

Keeping count with a tally

The hardest part is not the subtracting but keeping track of how many times you subtracted. Children often lose count or count the starting number by mistake.

A simple fix is a two-column table. Write the subtraction on the left and a tally mark on the right. At the end, count only the tally marks. For bigger numbers, write a 1 beside each step and add them up.

Counters help too. Take away a group of counters, put it in a pot, and at the end count the pots.

When you can’t reach 0

Try 17 ÷ 5: 17 − 5 = 12, 12 − 5 = 7, 7 − 5 = 2. Now 2 is less than 5, so you can’t take away another 5. You subtracted 3 times with 2 left over: 17 ÷ 5 = 3 r 2.

The rule for stopping is the same rule as in all division: the remainder must be smaller than the divisor. Read more in division with remainders.

Faster: take away bigger chunks

Repeated subtraction gets slow with big numbers. 96 ÷ 4 would take 24 steps. Instead, take away a bigger chunk of 4s at once: 10 fours is 40.

96 − 40 = 56 (10 fours), 56 − 40 = 16 (10 more fours), 16 − 16 = 0 (4 fours). Add the counts: 10 + 10 + 4 = 24. So 96 ÷ 4 = 24.

This faster version has its own name, partial quotients, and it is a common grade 4 and 5 method. Repeated subtraction is where it starts.

Quiz: divide by taking away

Take the divisor away until you reach 0, and count the steps.

Where this fits: division step by step

  1. What is division
  2. Division as repeated subtraction (this page)
  3. Division on a number line
  4. Dividend, divisor and quotient
  5. Dividing by 2, 5 and 10
  6. Division facts
  7. Checking division with multiplication
  8. Division with remainders
  9. Interpreting remainders
  10. 2-digit by 1-digit division
  11. 3-digit by 1-digit division
  12. Partial quotients
  13. Short division
  14. Long division
  15. Zeros in the quotient
  16. Estimating quotients
  17. Long division with 2-digit divisors
  18. Division word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “Here are 15 blocks. Make a tower of 3 and move it to the side.”
  2. “How many are left?” (12.) “Make another tower of 3.”
  3. “Keep going until there are none left.” (Makes 5 towers.)
  4. “How many towers?” (5.) “So 15 ÷ 3 = 5. We took away 3, five times.”
  5. “What if we started with 16?” (5 towers and 1 left over!)

More worked examples

Example 1: 12 ÷ 4

12 − 4 = 8, 8 − 4 = 4, 4 − 4 = 0. Three subtractions, so 12 ÷ 4 = 3.

Example 2: 30 ÷ 6

30, 24, 18, 12, 6, 0. Five subtractions, so 30 ÷ 6 = 5.

Example 3: with a remainder: 23 ÷ 4

23, 19, 15, 11, 7, 3. Five subtractions, and 3 is less than 4. 23 ÷ 4 = 5 r 3.

Example 4: bigger chunks: 84 ÷ 7

84 − 70 = 14 (10 sevens), 14 − 14 = 0 (2 sevens). 10 + 2 = 12, so 84 ÷ 7 = 12.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. 8 ÷ 2
  2. 15 ÷ 5
  3. 12 ÷ 3
  4. 24 ÷ 6
  5. 28 ÷ 7
  6. 27 ÷ 9
  7. 19 ÷ 5
  8. 26 ÷ 4
  9. How many 8s can you take from 40?
  10. Stretch: 75 ÷ 5 using chunks of 50 and 25
Show the answers
  1. 4
  2. 3
  3. 4
  4. 4
  5. 4
  6. 3
  7. 3 r 4
  8. 6 r 2
  9. 5
  10. 10 + 5 = 15

Common mistakes

Counting the startCounts 20, 15, 10, 5, 0 as five steps for 20 ÷ 5.Fix: count the subtractions, not the numbers. Use a tally mark for each one.
Stopping too earlyStops at 5 in 20 ÷ 5 and says 3.Fix: keep going while what is left is as big as the divisor.
A remainder too bigSays 17 ÷ 5 = 2 r 7.Fix: 7 is bigger than 5, so take away one more 5: 3 r 2.

How to teach it at home

Tower building

Build towers of the same height from a pile of blocks and count them.

Coin piles

Take 5p or 5-cent coins away from a pile in equal stacks.

Countdown

Count back from 30 in 3s together and keep score on your fingers.

By grade

More for each grade: Grade 3 math and the CBSE class 3 maths guide.

Worksheets and practice

Division facts worksheet, page 1

Division facts worksheet: printable PDF with an answer key. · Make a fresh test

Division practice · division speed test · division chart · division for kids

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Questions parents ask

What is division as repeated subtraction?

Taking the divisor away from the dividend again and again until you reach 0, then counting the subtractions. 20 − 5 − 5 − 5 − 5 = 0, so 20 ÷ 5 = 4.

How do you find the remainder with repeated subtraction?

Stop when what is left is smaller than the divisor. That amount is the remainder: 17 ÷ 5 = 3 r 2.

Is repeated subtraction the same as grouping?

Yes. Each subtraction takes away one group of the divisor, so counting them counts the groups.

Why is repeated subtraction slow for big numbers?

Because each step only takes one group. Taking away chunks of 10 or 100 groups at once, called partial quotients, is much faster.

What grade learns division by repeated subtraction?

Grade 3 (class 3), when division is first introduced.