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 $\frac{2}{3}a=16$.

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

$\frac{2}{3}\times \frac{3}{2} =1$

To solve for a let us divide 16 by $\frac{2}{3}$.

$a=16\div \frac{2}{3}$

Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by $\frac{3}{2}$.

$a=16\times\frac{3}{2}$

$a=8\times 3$

$a=24$

We can see that to solve for a we have multiplied 16 by $\frac{3}{2}$ and $\frac{3}{2}$ is reciprocal of $\frac{2}{3}$.

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

$\frac{2}{3}\times 24=16$

$2\times 8=16$

$16=16$

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