Question 1 - Page 125 - Shortcut for Divisibility by 9 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 1 - Page 125 Look at each of the following statements. Which are correct and why? (i) If a number is divisible by 9, then the sum of its digits is divisible by 9.This is the main rule. Example: 18 is divisible by 9, and 1 + 8 = 9 Thus, the statement is true Question 1 - Page 125 Look at each of the following statements. Which are correct and why? (ii) If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.The rule works both ways. If the sum of digits fit perfectly into 9, the big number does too. Example: For 1809 Sum of digits = 1 + 8 + 0 + 9 = 18 Since 18 is divisible by 9, ∴ 1809 is divisible by 9 Thus, the statement is true Question 1 - Page 125 Look at each of the following statements. Which are correct and why? (iii) If a number is not divisible by 9, then the sum of its digits is not divisible by 9.Let’s take an example 13 is not divisible by 9. Sum of digits = 1 + 3 = 4 ∴ Sum of digits is also not divisible by 9. Thus, the statement is true Question 1 - Page 125 Look at each of the following statements. Which are correct and why? (iv) If the sum of the digits of a number is not divisible by 9, then the number is not divisible by 9.Let’s take an example 23 is not divisible by 9 as Sum of digits = 2 + 3 = 5 Since Sum of digits is not divisible by 9 ∴ Number 23 is not divisible by 9 Thus, the statement is true