Question

Simplify:
$[(\frac{2}{3})+(\frac{4}{5}\div\frac{2}{7})]\div [(\frac{3}{2})-(\frac{5}{6}\times\frac{3}{4})]$

• A. 416/105
• B. 418/110
• C. 425/250
• D. 526/350

Answer 1

Answer:

A. 416/105

Simplify:

[
\left[\frac{2}{3}+\left(\frac{4}{5}\div\frac{2}{7}\right)\right]\div\left[\frac{3}{2}-\left(\frac{5}{6}\times\frac{3}{4}\right)\right]
]

Step 1: Simplify the first bracket

[
\frac{4}{5}\div\frac{2}{7}
= \frac{4}{5}\times\frac{7}{2}
= \frac{28}{10}
= \frac{14}{5}
]

Now,

$\frac{2}{3}+\frac{14}{5}$
$= \frac{10}{15}+\frac{42}{15}$
$= \frac{52}{15}$

Simplify the second bracket

$\frac{5}{6}\times\frac{3}{4}$
$= \frac{15}{24}$
$= \frac{5}{8}$

Now,

$\frac{3}{2}-\frac{5}{8}$
$= \frac{12}{8}-\frac{5}{8}$
$= \frac{7}{8}$

Divide the two results

$\frac{52}{15}\div\frac{7}{8}$
$= \frac{52}{15}\times\frac{8}{7}$
$= \frac{416}{105}$

Since 416 and 105 have no common factor, the fraction is already in simplest form.

Answer:

$\boxed{\frac{416}{105}}$