NCERT Solutions – Class 8 Maths (Ganita Prakash)
Chapter: Number Play
Exercise 5.3
1. Find, without dividing, whether the following numbers are divisible by 9:
Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.
- (i) 123 → 1 + 2 + 3 = 6 → Not divisible by 9
- (ii) 405 → 4 + 0 + 5 = 9 → Divisible by 9
- (iii) 8888 → 8 + 8 + 8 + 8 = 32 → Not divisible by 9
- (iv) 93547 → 9 + 3 + 5 + 4 + 7 = 28 → Not divisible by 9
- (v) 358095 → 3 + 5 + 8 + 0 + 9 + 5 = 30 → Not divisible by 9
2. Find the smallest multiple of 9 with no odd digits:
Allowed digits: 0, 2, 4, 6, 8
Try smallest numbers:
0 → divisible by 9 and has no odd digit
Answer: 0
3. Find the multiple of 9 that is closest to 6000:
6000 ÷ 9 = 666 remainder 6
Nearby multiples:
- 9 × 666 = 5994
- 9 × 667 = 6003
Check closeness:
- 6000 − 5994 = 6
- 6003 − 6000 = 3
Answer: 6003 (closer)
4. How many multiples of 9 are there between 4300 and 4400?
First multiple ≥ 4300:
4302 = 9 × 478
Last multiple ≤ 4400:
4392 = 9 × 488
Total count:
= 488 − 478 + 1 = 11
Answer: 11 multiples