Question

The multiplicative inverse of (9 /16 × −4 /3) is​

Answer 1

Answer:

$-\frac{16}{9}\:\times \frac{3}{4}$

Step-by-step explanation:

$-\frac{16}{9}\times \frac{3}{4}=-\frac{4}{3}\quad \left(\mathrm{Decimal:\quad }\:-1.33333\dots \right)$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}$

$\frac{16}{9}\times \frac{3}{4}=\frac{16\times \:3}{9\times \:4}$

$=-\frac{16\times \:3}{9\times \:4}$

$\mathrm{Factor\:the\:number:\:}\:16=4\times \:4$

$=-\frac{4\times \:4\times \:3}{9\times \:4}$

$\mathrm{Cancel\:the\:common\:factor:}\:4$

$=-\frac{4\times \:3}{9}$

$\mathrm{Factor\:the\:number:\:}\:9=3\times \:3$

$=-\frac{4\times \:3}{3\times \:3}$

$\mathrm{Cancel\:the\:common\:factor:}\:3$

$=-\frac{4}{3}$