Problem 80 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$7 \cdot(11 \cdot 8)=(11 \cdot 8) \cdot 7$$

Step-by-Step Solution

Answer

The property illustrated is the Commutative Property of Multiplication.

Step 1: Recognize the structures

Check the given equation very carefully. It can be seen that it involves two operations of multiplication and on both sides of the equality, the same numbers are used, but with different orders.

Step 2: Identify the difference in the structure

The left-hand side starts with multiplying 7 with the product of 11 and 8, while the same operation on the right-hand side switches the order to start with the product of 11 and 8 first, then followed by multiplying by 7. However, the operation doesn't change its position. Hence, it's not an associative property but likely a commutative property.

Step 3: Determine the property

The commutative property of multiplication states that the product of two numbers remains the same even if the order of multiplicants changes.