Question

actor of 111.
2. Explain the following statements with suitable examples.
a) If a number is divisible by 9, it will also be divisible by 3.
b) If a number is divisible by 10, it will also be divisible by 5.
3​

Answer 1

Answer ⤵️

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.

Consider the following numbers which are divisible by 9, using the test of divisibility by 9:

99, 198, 171, 9990, 3411.

(i) 99

Sum of the digits of 99 = 9 + 9 = 18, which is divisible by 9.

Hence, 99 is divisible by 9.

(ii) 198

Sum of the digits of 198 = 1 + 9 + 8 = 18, which is divisible by 9.

Hence, 198 is divisible by 9.

(iii) 171

Sum of the digits of 171 = 1 + 7 + 1 = 9, which is divisible by 9.

Hence, 171 is divisible by 9.

(iv) 9990

Sum of the digits of 9990 = 9 + 9 + 9+ 0 = 27, which is divisible by 9.

Hence, 9990 is divisible by 9.

(v) 3411

Sum of the digits of 3411 = 3 + 4 + 1+ 1 = 9, which is divisible by 9.

Hence, 3411 is divisible by 9.

Consider the following numbers which are not divisible by 9, using the rules of divisibility by 9:

73, 237, 394, 1277, 1379.

(i) 73

Sum of the digits of 73 = 7 + 3 = 10, which is not divisible by 9.

Hence, 73 is not divisible by 9.

(ii) 237

Sum of the digits of 237 = 2 + 3 + 7 = 12, which is not divisible by 9.

Hence, 237 is not divisible by 9.

(iii) 394

Sum of the digits of 394 = 3 + 9 + 4 = 16, which is not divisible by 9.

Hence, 394 is not divisible by 9.

(iv) 1277

Sum of the digits of 1277 = 1 + 2 + 7 + 7 = 17, which is not divisible by 9.

Hence, 1277 is not divisible by 9.

(v) 1379

Sum of the digits of 1379 = 1 + 3 + 7 + 9 = 20, which is not divisible by 9.

Hence, 1379 is not divisible by 9.

1. Choose the numbers which are divisible by 9.

13 27 128 65 730363 900 1375

Answer: 27, 900