Which property is illustrated by the following statement?
(3z)xy = 3(zx)y
The property illustrated by the statement is the associative property of multiplication.
The property illustrated by the given statement is the Associative Property of Multiplication. This property states that the grouping of factors in a multiplication expression does not affect the result. In this case, the factors (3z), x, and y are grouped differently but the result is the same, demonstrating the Associative Property of Multiplication.
The property illustrated by the given statement is the associative property of multiplication.
To understand this property, let's break down the given statement:
(3z)xy = 3(zx)y
In mathematics, the associative property states that the way in which numbers are grouped does not affect the result of multiplication. In other words, changing the grouping of the factors will produce the same result.
To see this in action, let's evaluate the expression step by step:
1. Start with the left side: (3z)xy
Since the parentheses indicate multiplication, we can first multiply 3 and z: 3z. Then, we multiply the result by xy: (3z)xy.
2. Now, evaluate the right side: 3(zx)y
Similarly, multiplying z and x gives zx. Then, we multiply that by y: 3(zx)y.
Comparing the two expressions, we can see that they are the same: (3z)xy = 3(zx)y. This demonstrates the associative property of multiplication, where we can change the grouping of factors without changing the result.