Question Which property is illustrated by the following statement? (3z)xy = 3(zx)y (1 point)
The property illustrated by the given statement is the associative property of multiplication.
The property that is illustrated by the following statement is the Associative Property.
To determine which property is illustrated by the statement (3z)xy = 3(zx)y, we can analyze the equation and compare the two sides.
From the equation, we can see that the terms (3z), x, and y are grouped inside brackets on the left side of the equation, while on the right side, the terms (zx) and y are grouped inside brackets.
The property being illustrated here is the Associative Property of Multiplication. This property states that the grouping of factors being multiplied does not affect the product.
To explain how to get the answer, we can break it down into steps:
Step 1: Start with the given equation: (3z)xy = 3(zx)y
Step 2: Observe the grouping of factors on the left side, where (3z) is grouped together and then multiplied by x and y.
Step 3: Similarly, on the right side, (zx) is grouped together and then multiplied by y.
Step 4: Apply the Associative Property of Multiplication, which states that changing the grouping of factors being multiplied will not affect the product. Therefore, we can rearrange or regroup the factors as necessary.
Step 5: By applying the Associative Property of Multiplication, we can conclude that (3z)xy is equal to 3(zx)y, and vice versa. Hence, the property illustrated by the statement is the Associative Property of Multiplication.