Question

What number must we multiply by $-\frac23$ to get a product of $\frac34$?

Answer 1

Let x be unknown number. If number x is multiplied by $-\dfrac{2}{3}$ and the product is equal to $\dfrac{3}{4},$ then

$x\cdot \left(-\dfrac{2}{3}\right)=\dfrac{3}{4}.$

To find x you should divide $\dfrac{3}{4}$ by $-\dfrac{2}{3}:$

$x=\dfrac{\dfrac{3}{4}}{-\dfrac{2}{3}}=\dfrac{3}{4}\cdot \left(-\dfrac{3}{2}\right)=-\dfrac{3\cdot 3}{4\cdot 2}=-\dfrac{9}{8}.$

Answer: $x=-\dfrac{9}{8}$