Question

given that 2/3a=16, which of the following illustrates how the multiplicative inverse property can be used to find the value of a?

Answer 1

multiplying both side by 3/2
2/3a×3/2 = 16×3/2
a= 8×3 = 24

Answer 2

Step-by-step explanation:

We have been given that
`(2)/(3)a=16`.

Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.

`(2)/(3)* (3)/(2) =1`

To solve for a let us divide 16 by
`(2)/(3)`.

`a=16/ (2)/(3)`

Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by
`(3)/(2)`.

`a=16*(3)/(2)`

`a=8* 3`

`a=24`

We can see that to solve for a we have multiplied 16 by
`(3)/(2)` and
`(3)/(2)` is reciprocal of
`(2)/(3)`.

Let us verify our answer by substituting a=24 in our given equation.

`(2)/(3)* 24=16`

`2* 8=16`

`16=16`

Hence, to find the value of a we used multiplicative inverse property.