Solve 3/4+5/8/frac{3{5}(1/4+frac{2}{3})}

$$\frac { \frac { 3 } { 4 } + \frac { 5 } { 8 } } { \frac { 3 } { 5 } ( \frac { 1 } { 4 } + \frac { 2 } { 3 } ) }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{6}{8}+\frac{5}{8}}{\frac{3}{5}\left(\frac{1}{4}+\frac{2}{3}\right)}$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6+5}{8}}{\frac{3}{5}\left(\frac{1}{4}+\frac{2}{3}\right)}$$

Add 6 and 5 to get 11.

$$\frac{\frac{11}{8}}{\frac{3}{5}\left(\frac{1}{4}+\frac{2}{3}\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{\frac{11}{8}}{\frac{3}{5}\left(\frac{3}{12}+\frac{8}{12}\right)}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{8}}{\frac{3}{5}\times \frac{3+8}{12}}$$

Add 3 and 8 to get 11.

$$\frac{\frac{11}{8}}{\frac{3}{5}\times \frac{11}{12}}$$

Multiply \frac{3}{5} times \frac{11}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{11}{8}}{\frac{3\times 11}{5\times 12}}$$

Do the multiplications in the fraction \frac{3\times 11}{5\times 12}.

$$\frac{\frac{11}{8}}{\frac{33}{60}}$$

Reduce the fraction \frac{33}{60} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{8}}{\frac{11}{20}}$$

Divide \frac{11}{8} by \frac{11}{20} by multiplying \frac{11}{8} by the reciprocal of \frac{11}{20}.

$$\frac{11}{8}\times \frac{20}{11}$$

Multiply \frac{11}{8} times \frac{20}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 20}{8\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$