Question

1 .State wheather true or false (a). Rational number are associative under subtrction and division.​

Answer 1

Answer: False

Step-by-step explanation:

According to associative property, you can add/multiply numbers regardless of how the numbers are grouped.

a + (b + c) = (a + b) + c

a × (b × c) = (a × b) × c

However, this rule doesn't apply to subtraction and division.

a - (b - c) ≠ (a - b) - c

E.g. 3 - (2 - 1) = 3 - 1 = 2 ; (3 - 2) - 1 = 1 - 1 = 0

Here, we can see, 2 ≠ 0.

a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

E.g. 8 ÷ (4 ÷ 2) = 8 ÷ 2 = 4 ; (8 ÷ 4) ÷ 2 = 2 ÷ 2 = 1

Here, we can see, 4 ≠ 1.

Therefore, rational numbers are not associative under subtraction and division.