Is Multiplication Associative for Rational Numbers?


Question: Is multiplication associative for rational numbers?

The multiplication is commutative and associative in the set of rational numbers.

Answer: The multiplication is associative in the set of rational numbers. 

Let's understand the associative property in detail.

Explanation:

The associative property states that we can add or multiply the given terms regardless of the order or how we group the numbers.

i.e, (a × b) × c = a × (b × c)

For example, 1/2 × (1/3 × 1/4) = 1/2 × (1/12) = 1/24

is the same as (1/2 ×1/3)  × 1/4 = (1/6) × 1/4 = 1/24

Thus, 1/2 × (1/3 × 1/4) = (1/2 ×1/3)  × 1/4

Therefore, the final product is the same regardless of how the numbers are grouped.

Thus, the multiplication of rational numbers is associative.