Question

Solve $(\frac{7}{8}-\frac{6}{15})÷(\frac{11}{22}+\frac{9}{15}\times \frac{5}{7})$

• A. $\frac{133}{260}$
• B. $\frac{260}{133}$
• C. $1\frac{127}{133}$

Answer 1

The correct option is A $\frac{133}{260}$

Using PEMDAS rule, we must first evaluate the expression inside the paranthesis.

$(\frac{11}{22}+\frac{9}{15}\times \frac{5}{7})$
(evaluating muliplication before addition)

$=(\frac{11}{11\times 2}+\frac{3\times 3}{5\times 3}\times \frac{5}{7})$
(canceling the common terms from numerator and denominator)

$=(\frac{1}{2}+\frac{3}{7})=\left(\frac{1\times 7+3\times 2}{14}\right)=\left(\frac{7+6}{14}\right)=\frac{13}{14}$

$\text{Now, evaluate}(\frac{7}{8}-\frac{6}{15})=(\frac{7}{8}-\frac{2\times 3}{5\times 3})=(\frac{7}{8}-\frac{2}{5})=\frac{7\times 5-2\times 8}{8\times 5}=\frac{35-16}{40}=\frac{19}{40}$

$\therefore (\frac{7}{8}-\frac{6}{15})÷(\frac{11}{22}+\frac{9}{15}\times \frac{5}{7})=\frac{19}{40}÷\frac{13}{14}=\frac{19\times 14}{40\times 13}=\frac{19\times 2\times 7}{2\times 20\times 13}=\frac{19\times 7}{20\times 13}=\frac{133}{260}$