Choose the property illustrated by the following statement.
(9•y)•6=9•(y•6)
(A) Associative property of multiplication
(B) commutative property of multiplication
(C) distributive property
(D) identity element of multiplication
Could you explain how you got the answer as well? Thank You
The property illustrated by the given statement is the associative property of multiplication, which is option (A).
To understand this, let's break down the statement: (9•y)•6 = 9•(y•6).
The associative property of multiplication states that when multiplying three or more numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the numbers being multiplied without changing the final product.
In the given statement, both sides of the equation involve three numbers being multiplied (9, y, and 6).
On the left side: (9•y)•6 means multiplying 9 and y first, and then multiplying the result by 6.
On the right side: 9•(y•6) means multiplying y and 6 first, and then multiplying the result by 9.
Regardless of the grouping of the numbers, the associative property allows us to switch the order of operations, so the result will be the same.
Therefore, the statement (9•y)•6 = 9•(y•6) demonstrates the associative property of multiplication.