Question

Simplify: $\frac{\frac{3}{5}+\frac{1}{3}}{\frac{2}{3}+\frac{2}{5}}$

• A. $\frac{3}{4}$
• B. $\frac{4}{5}$
• C. $\frac{6}{7}$
• D. $\frac{7}{8}$

Answer 1

The correct option is D $\frac{7}{8}$

First, add the fractions in the numerator and denominator:

$\frac{\frac{14}{15}}{\frac{16}{15}}=\frac{14}{15}\times \frac{15}{16}=\frac{14}{16}=\frac{7}{8}$

Alternatively, to save time, multiply each of the small fractions by 15,which is

the common denominator of all the fractions in the problem. Because you are

multiplying the numerator and the denominator of the whole complex fraction by 15,you are not changing its value:

$\frac{9+5}{10+6}=\frac{14}{16}=\frac{7}{8}$