Division as Repeated Subtraction
Just as multiplication is repeated addition, division is repeated subtraction. You keep subtracting the same number until you reach 0 (or a number smaller than the divisor). The number of times you subtract gives the quotient.
This method helps you understand why division works, before you start using tables to divide quickly.
What is Division as Repeated Subtraction - Class 3 Maths (Division)?
Division as repeated subtraction means subtracting the divisor from the dividend again and again until you cannot subtract anymore. The count of subtractions is the quotient.
Keep subtracting the divisor until you reach 0. Count the steps = Quotient.
Solved Examples
Example 1: Basic Repeated Subtraction
Question: Find 12 ÷ 3 by repeated subtraction.
Think:
- 12 − 3 = 9 (1st subtraction)
- 9 − 3 = 6 (2nd subtraction)
- 6 − 3 = 3 (3rd subtraction)
- 3 − 3 = 0 (4th subtraction)
- We subtracted 3 four times.
Answer: 12 ÷ 3 = 4.
Example 2: Divide by 2
Question: Find 10 ÷ 2 by repeated subtraction.
Think:
- 10 − 2 = 8 → 8 − 2 = 6 → 6 − 2 = 4 → 4 − 2 = 2 → 2 − 2 = 0
- We subtracted 2 five times.
Answer: 10 ÷ 2 = 5.
Example 3: Divide by 5
Question: Find 20 ÷ 5 by repeated subtraction.
Think:
- 20 − 5 = 15 → 15 − 5 = 10 → 10 − 5 = 5 → 5 − 5 = 0
- 4 subtractions
Answer: 20 ÷ 5 = 4.
Example 4: Word Problem — Sharing Mangoes
Question: Kavi has 18 mangoes. He gives away 6 at a time to friends. How many friends get mangoes?
Think:
- 18 − 6 = 12 (1 friend)
- 12 − 6 = 6 (2 friends)
- 6 − 6 = 0 (3 friends)
Answer: 3 friends get mangoes.
Example 5: Divide by 4
Question: Find 24 ÷ 4 by repeated subtraction.
Think:
- 24 − 4 = 20 → 20 − 4 = 16 → 16 − 4 = 12 → 12 − 4 = 8 → 8 − 4 = 4 → 4 − 4 = 0
- 6 subtractions
Answer: 24 ÷ 4 = 6.
Example 6: Using a Number Line
Question: Show 15 ÷ 3 on a number line.
Think:
0 — 3 — 6 — 9 — 12 — 15
Start at 15 and jump back by 3 each time: 15 → 12 → 9 → 6 → 3 → 0. That is 5 jumps.
Answer: 15 ÷ 3 = 5.
Example 7: With Remainder
Question: Find 14 ÷ 4 by repeated subtraction.
Think:
- 14 − 4 = 10 → 10 − 4 = 6 → 6 − 4 = 2
- We cannot subtract 4 from 2.
- 3 subtractions with 2 left over.
Answer: 14 ÷ 4 = 3 remainder 2.
Example 8: Comparing with Multiplication
Question: Verify 21 ÷ 7 = 3 using repeated subtraction.
Think:
- 21 − 7 = 14 → 14 − 7 = 7 → 7 − 7 = 0
- 3 subtractions → quotient = 3
- Check: 7 × 3 = 21 ✓
Answer: 21 ÷ 7 = 3. Verified.
Example 9: Word Problem — Packing Boxes
Question: Aditi has 30 books. She packs 5 books in each box. How many boxes does she need?
Think:
- 30 − 5 = 25 → 25 − 5 = 20 → 20 − 5 = 15 → 15 − 5 = 10 → 10 − 5 = 5 → 5 − 5 = 0
- 6 subtractions
Answer: Aditi needs 6 boxes.
Example 10: Why Repeated Subtraction Works
Question: Explain why 16 ÷ 4 = 4 using repeated subtraction.
Think:
- 16 − 4 = 12 (1st) → 12 − 4 = 8 (2nd) → 8 − 4 = 4 (3rd) → 4 − 4 = 0 (4th)
- Each subtraction removes one group of 4.
- There are exactly 4 groups of 4 in 16.
Answer: 16 ÷ 4 = 4 because 16 contains exactly 4 groups of 4.
Key Points to Remember
- Division as repeated subtraction means subtracting the divisor from the dividend until you reach 0.
- The number of times you subtract = the quotient.
- If a number is left over that is smaller than the divisor, it is the remainder.
- This method can be shown on a number line by jumping backwards.
- Repeated subtraction works the same way as multiplication tables in reverse.
- This method is useful for understanding division before memorising tables.
Practice Problems
- Find 16 ÷ 2 by repeated subtraction.
- Find 27 ÷ 9 by repeated subtraction.
- Neha has 35 beads. She takes out 7 at a time. How many times does she take out beads?
- Show 20 ÷ 4 on a number line.
- Find 17 ÷ 5 by repeated subtraction. What is the remainder?
- Aman has 40 stickers. He gives 8 to each friend. How many friends get stickers?
- Find 32 ÷ 8 by repeated subtraction and verify using multiplication.
Frequently Asked Questions
Q1. What does division as repeated subtraction mean?
It means you subtract the divisor from the dividend again and again until you reach 0 or a number smaller than the divisor. The count of subtractions is the quotient.
Q2. How is repeated subtraction related to division?
They give the same answer. 12 ÷ 4 means how many times can you subtract 4 from 12. The answer is 3 (since 12 − 4 − 4 − 4 = 0).
Q3. What happens if there is something left over?
The amount left over is the remainder. For example, 14 ÷ 3: you subtract 3 four times to get 2 left over. So the quotient is 4 with remainder 2.
Q4. Can I show repeated subtraction on a number line?
Yes. Start at the dividend and jump backwards by the divisor each time. Count the jumps to find the quotient.
Q5. Is repeated subtraction a slow method?
It can be slow for large numbers. That is why you learn multiplication tables — they let you divide quickly. But repeated subtraction helps you understand what division really means.
Q6. Why do we learn this method?
It builds a strong understanding of division as taking away equal groups. Once you understand the concept, using tables becomes easier and faster.
Q7. Does repeated subtraction always reach exactly 0?
Not always. If the dividend is not a multiple of the divisor, you stop when the number left is smaller than the divisor. That leftover is the remainder.
Q8. Is this method in the NCERT Class 3 textbook?
Yes. NCERT Class 3 Maths introduces division through grouping and repeated subtraction before moving to using tables.
