Associative Property for Multiplication

Rule for the associative property of multiplication is:

(xy) z = x (yz)

On solving 5×3×2, we get 30 as a product. Now as in addition, let’s group the terms:

⇒ (5 × 3) × 2 = 15 × 2 = 30         (BODMAS rule)

After regrouping,

⇒ 5 × (3 × 2) = 5 × 6 = 30

Products will be the same.

Thus, addition and multiplication are associative in nature but subtraction and division are not associative.

For example, divide 100 ÷ 10 ÷ 5

⇒ (100 ÷ 10) ÷ 5 ≠ 100 ÷ (10 ÷ 5)

⇒ (10) ÷ 5 ≠ 100 ÷ (2)

⇒ 2 ≠ 50

Subtract, 3 − 2 − 1

⇒ (3 − 2) − 1 ≠ 3 − (2 − 1)

⇒ (1) – 1 ≠ 3 − (1)

⇒ 0 ≠ 2

Hence, proved the associative property is not applicable for subtraction and division methods.