Question

By what rational number should we multiply $\frac{20}{-9}$, so that the product may be $\frac{-5}{9}$ ?

Answer 1

Step 1: Using the concept of multiplication of rational numbers
Let, the required number be $x$.
According to the given question, product of $x$
and $\frac{20}{-9}$is$\frac{-5}{9}$
i.e.,$x\times \frac{20}{-9}=\frac{-5}{9}$
$x\times \frac{20}{9}=\frac{5}{9}-------\left(i\right)$
Step 2: Simplify the given equation to get required unknown.
From (i),$x\times \frac{20}{9}=\frac{5}{9}$
$x=\frac{5}{9}/\frac{20}{9}$
$x=\frac{5}{9}\times \frac{9}{20}$
$x=\frac{5\times 9}{9\times 20}$
$x=\frac{1}{4}$

Hence,$\frac{1}{4}$should we multiply$\frac{20}{-9}$so that the product is $\frac{-5}{9}$.