Determine whether the statements below are ‘Always True’, ‘Sometimes True’, or ‘Never True’. Explain your reasoning. Class 8

Determine whether the statements below are ‘Always True’, ‘Sometimes True’, or ‘Never True’. Explain your reasoning. Class 8

Question 1.

Determine whether the statements below are ‘Always True’, ‘Sometimes True’, or ‘Never True’. Explain your reasoning.

(i) The product of a multiple of 6 and a multiple of 3 is a multiple of 9.

(ii) The sum of three consecutive even numbers will be divisible by 6.

(iii) If abcdef is a multiple of 6, then badcef will be a multiple of 6.

(iv) 8 (7b - 3) - 4 (11b + 1) is a multiple of 12.

Solution:

(i) Always true, because product of 6 and 3 is 18, which is a multiple of 9.

(ii) Always true, because sum of any three consecutive numbers is divisible by 3 and even numbers are divisible by 2.

(iii) Always true, because sum of the digits will remain a multiple of 3 and f at the unit place is already even.

(iv) 8 (7b - 3) - 4 (11b + 1)

= 56b - 24 - 44b - 4

= 126 - 28.

So, it is not a multiple of 12.