Question

Multiply $\frac{6}{13}$by the reciprocal of $-\frac{7}{16}$.

Answer 1

Step 1: Find the reciprocal of $-\frac{7}{16}$.

We know that the reciprocal or multiplicative inverse of the rational number $\frac{a}{b}$ is $\frac{c}{d}$ if $\frac{a}{b}\times \frac{c}{d}=1$.

Let $\frac{c}{d}$is a reciprocal of $-\frac{7}{16}$.

Therefore,

$\begin{array}{l} -\frac{7}{16}\times \frac{c}{d}=1\\ \Rightarrow \frac{c}{d}=-\frac{16}{7}\end{array}$

Step 2: Multiply $\frac{6}{13}$by the reciprocal of $-\frac{16}{7}$.

$\begin{array}{l}=\frac{6}{13}\times -\frac{16}{7}\\ =-\frac{96}{91}\end{array}$

Hence the Multiplication of $\frac{6}{13}$by the reciprocal of $-\frac{7}{16}$is $-\frac{96}{91}$.