Problem 78 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$6 \cdot(2 \cdot 3)=6 \cdot(3 \cdot 2)$$

Step-by-Step Solution

Answer

The property illustrated is the Commutative Property of Multiplication.

Step 1: Identify the operations in the exercise

First, notice that the operations used in the equation are multiplication. Therefore, the property has to be one that relates to multiplication.

Step 2: Spot the difference and similarity in both sides

Examine the equation - On both sides, the same numbers 6, 2 and 3 are being multiplied. The only difference is the order in which 2 and 3 are multiplied. Despite this difference, the two expressions are equal.

Step 3: Identify the property

The fact that the order of multiplication does not affect the outcome indicates the property being illustrated is the Commutative Property of Multiplication. This property states that changing the order of the numbers we are multiplying does not change the product.