Question

Identify the property that the statement illustrates.

$(3 · 8) · 2= 3 · (8 · 2)$

Short answer

The statement$(3 · 8) ·2 = 3 · (8 · 2)$illustrates the Associative Property of Multiplication.

Step-by-step solution

Step-1 – Apply the concept of product

When two or more numbers are multiplied together, it gives a number. The numbers that are being multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

Step-2 – Associative Property of Multiplication of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · ( \text{b} · \text{c} )$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · ( \text{4} · \text{3} ) = 72$

Step-3:  Identify the property that the statement (3 x 8) x 2 = 3 (8 x 2) illustrates.

Associative property of Multiplication states that if you are multiplying three real numbers, the product is always the same regardless of their grouping.

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · ( \text{b} · \text{c} )$

The statement $(3 · 8) ·2 = 3 · (8 · 2)$illustrates the Associative Property of Multiplication.