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

Since the multiplicative inverse of a fraction p/q is the fraction that swaps its numerator and denominator, i.e. q/p, we have that the inverse of 2/3 is 3/2.

So, if we multiply both sides of the equation by 3/2, we have

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

3/2 and 2/3 are multiplicative inverse of each other, and by definition this means that they give 1 when multiplied:

`(3)/(2)\cdot(2)/(3)a=1\cdot a=a=16\cdot(3)/(2)`

On the right hand side, we have

`16\cdot(3)/(2)=8\cdot 3=24`

And so the solution is
`a=24`