Question

Simplify :
$(\frac{5}{6}+\frac{3}{4})\div(\frac{7}{8}-\frac{1}{3})$

• A. 38/13
• B. 48/13
• C. 58/13
• D. 68/13

Answer 1

Answer:

A. 38/13

Simplify:

$\left(\frac{5}{6}+\frac{3}{4}\right)\div\left(\frac{7}{8}-\frac{1}{3}\right)$

Step 1: Add the fractions in the numerator

LCM of 6 and 4 is 12.

$\frac{5}{6}=\frac{10}{12},\qquad \frac{3}{4}=\frac{9}{12}$

$\frac{10}{12}+\frac{9}{12}=\frac{19}{12}$

Subtract the fractions in the denominator

LCM of 8 and 3 is 24.

$\frac{7}{8}=\frac{21}{24},\qquad \frac{1}{3}=\frac{8}{24}$

$\frac{21}{24}-\frac{8}{24}=\frac{13}{24}$

Divide the fractions

$\frac{19}{12}\div\frac{13}{24}$
$=\frac{19}{12}\times\frac{24}{13}$

Simplify:

$\frac{24}{12}=2$

So,

$=\frac{19\times2}{13}$
$=\frac{38}{13}$