Question

Evaluate and simplify the following complex fraction. 9 − 5 − 3 8 = 8 −3 ​ −5 9 ​ ​ =start fraction, space, start fraction, 9, divided by, minus, 5, end fraction, space, divided by, start fraction, minus, 3, divided by, 8, end fraction, end fraction, equals

Answer 1

Answer:

$\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{24}{5}$

Step-by-step explanation:

Operations With Fractions

The division of the fractions \frac{a}{b} and \frac{c}{d} can be calculated by multiplying the first by the reciprocal of the second fraction:

$\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}*\frac{d}{c}$

We are given the following division of fractions:

$\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{9}{-5}*\frac{8}{-3}$

Multiplying and simplifying:

$\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{9}{5}*\frac{8}{3}$

$\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{9*8}{5*3}$

Simplifying by 3:

$\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{3*8}{5}$

$\mathbf{\displaystyle \frac{\frac{9}{-5}}{\frac{-3}{8}}=\frac{24}{5}}$