NCERT Solutions for Class 5th Maths Chapter 9 Splitting the number, and repeated halving — Mental Strategies for Division

Book page 123 Updated on2026-09-19

Q1.

Can you give 5 such examples where you can split the number conveniently?

Answer

Here are five. The idea is to break the dividend into parts that your tables already know.

Division	Split it like this	Divide each part	Answer
1236 ÷ 6	1200 + 36	200 + 6	206
728 ÷ 7	700 + 28	100 + 4	104
2408 ÷ 8	2400 + 8	300 + 1	301
4515 ÷ 5	4500 + 15	900 + 3	903
996 ÷ 4	1000 − 4	250 − 1	249

One worked out fully — 1236 ÷ 6:

Look for a nearby number that the divisor divides easily. 6 goes into 1200 nicely.
Split: 1236 = 1200 + 36.
Divide the first part: 1200 ÷ 6 = 200.
Divide the second part: 36 ÷ 6 = 6.
Add the two answers: 200 + 6 = 206.

Check by a second route: 6 × 206 = 1,236 ✓ 7 × 104 = 728 ✓ 8 × 301 = 2,408 ✓ 5 × 903 = 4,515 ✓ 4 × 249 = 996 ✓

Why splitting is allowed: If you share 1236 sweets among 6 children, you can hand out 1200 first and then the last 36. Each child ends up with the same total whichever way you hand them out.

Q2.

For which other divisors and dividends might this strategy of repeated halving work?

Answer

Repeated halving works whenever the divisor is 2, 4, 8, 16, 32 … — the numbers you get by doubling 2.

Divisor	How many times to halve	Example	Answer
2	once	86 → 43	86 ÷ 2 = 43
4	twice	128 → 64 → 32	128 ÷ 4 = 32
8	three times	96 → 48 → 24 → 12	96 ÷ 8 = 12
16	four times	320 → 160 → 80 → 40 → 20	320 ÷ 16 = 20

Why it happens: 4 is 2 × 2, so dividing by 4 is dividing by 2 and then by 2 again. 8 is 2 × 2 × 2, so you halve three times. Each halving undoes one of the twos.

The dividend must cooperate too. Halving 100 gives 50, halving 50 gives 25 — after that you cannot halve again and stay in whole numbers. So use it when the dividend keeps coming out even.

Did you know? You can mix the tricks. For ÷ 6, halve once and then divide by 3. Take 132 ÷ 6: half of 132 is 66, and 66 ÷ 3 = 22. Check: 6 × 22 = 132 ✓. In the same way ÷ 12 is halve, halve, then ÷ 3.

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