Which property is illustrated by the following statement?
(2x)yz = 2(xy)z
1. Associative Property of Multiplication
2. Commutative Property of Multiplication
3. Inverse Property of Multiplication
1. Associative Property of Multiplication
The property illustrated by the statement (2x)yz = 2(xy)z is the Associative Property of Multiplication.
The property illustrated by the statement (2x)yz = 2(xy)z is the Associative Property of Multiplication.
To understand why, let's break down the statement:
(2x)yz = 2(xy)z
In the left side of the equation, we have the expression (2x)yz, where 2x is enclosed in parentheses. On the right side, we have the expression 2(xy)z, where xy is enclosed in parentheses.
The Associative Property of Multiplication states that when multiplying three or more numbers, it does not matter which two numbers are multiplied first. In other words, the grouping of the numbers being multiplied does not affect the final result.
In this case, according to the property, we can change the grouping of the numbers and still get the same result:
(2x)yz = 2(xy)z
We can see that the numbers being multiplied are 2, x, y, and z. The property allows us to rearrange the grouping of these numbers, so we can rewrite the equation as:
2(xy)z = 2(xy)z
Since the equation remains the same after rearranging the grouping, we can conclude that the property illustrated by this statement is the Associative Property of Multiplication.