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Rule

Associative Property of Multiplication

The way three or more factors are grouped when multiplied does not affect the value of the product.

(a \cdot b) \cdot c = a \cdot (b \cdot c)

For example, consider the product

2 \cdot 4 \cdot 6 .

Grouping

2 \cdot 4

and multiplying it by

6

produces the same result as grouping

4 \cdot 6

and multiplying it by

2 .

(2 \cdot 4) \cdot 6 8 \cdot 6 ✓ 48 = 2 \cdot (4 \cdot 6) ⇓ = 2 \cdot 24 ⇓ = 48 ✓

Since the Associative Property of Multiplication is an axiom, it does not need a proof.

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