Question

Given that 2/3a = 16, which of the following illustrates how the multiplicative inverse

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

$\dfrac{3}{2}\cdot\dfrac{2}{3}a=16\cdot\dfrac{3}{2}$

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

$\dfrac{3}{2}\cdot\dfrac{2}{3}a=1\cdot a=a=16\cdot\dfrac{3}{2}$

On the right hand side, we have

$16\cdot\dfrac{3}{2}=8\cdot 3=24$

And so the solution is $a=24$