Solve 3/4divleft(1/2+5/8right)4/5

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

Evaluate

$$\frac{8}{15}\approx 0.533333333$$

Solution Steps

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{3}{4}}{\frac{4}{8}+\frac{5}{8}}\times \frac{4}{5}$$

Since \frac{4}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{4}}{\frac{4+5}{8}}\times \frac{4}{5}$$

Add 4 and 5 to get 9.

$$\frac{\frac{3}{4}}{\frac{9}{8}}\times \frac{4}{5}$$

Divide \frac{3}{4} by \frac{9}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{8}.

$$\frac{3}{4}\times \frac{8}{9}\times \frac{4}{5}$$

Multiply \frac{3}{4} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{4\times 9}\times \frac{4}{5}$$

Do the multiplications in the fraction \frac{3\times 8}{4\times 9}.

$$\frac{24}{36}\times \frac{4}{5}$$

Reduce the fraction \frac{24}{36} to lowest terms by extracting and canceling out 12.

$$\frac{2}{3}\times \frac{4}{5}$$

Multiply \frac{2}{3} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 4}{3\times 5}$$

Do the multiplications in the fraction \frac{2\times 4}{3\times 5}.

$$\frac{8}{15}$$

Factor

$$\frac{2 ^ {3}}{3 \cdot 5} = 0.5333333333333333$$