Solve 11/13div[(5/8+3/4)div5/8]

$$\frac { 11 } { 13 } \div [ ( \frac { 5 } { 8 } + \frac { 3 } { 4 } ) \div \frac { 5 } { 8 } ]$$

Evaluate

$$\frac{5}{13}\approx 0.384615385$$

Solution Steps

Divide \frac{11}{13} by \frac{\frac{5}{8}+\frac{3}{4}}{\frac{5}{8}} by multiplying \frac{11}{13} by the reciprocal of \frac{\frac{5}{8}+\frac{3}{4}}{\frac{5}{8}}.

$$\frac{11\times \frac{5}{8}}{13\left(\frac{5}{8}+\frac{3}{4}\right)}$$

Express 11\times \frac{5}{8} as a single fraction.

$$\frac{\frac{11\times 5}{8}}{13\left(\frac{5}{8}+\frac{3}{4}\right)}$$

Multiply 11 and 5 to get 55.

$$\frac{\frac{55}{8}}{13\left(\frac{5}{8}+\frac{3}{4}\right)}$$

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

$$\frac{\frac{55}{8}}{13\left(\frac{5}{8}+\frac{6}{8}\right)}$$

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

$$\frac{\frac{55}{8}}{13\times \frac{5+6}{8}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{55}{8}}{13\times \frac{11}{8}}$$

Express 13\times \frac{11}{8} as a single fraction.

$$\frac{\frac{55}{8}}{\frac{13\times 11}{8}}$$

Multiply 13 and 11 to get 143.

$$\frac{\frac{55}{8}}{\frac{143}{8}}$$

Divide \frac{55}{8} by \frac{143}{8} by multiplying \frac{55}{8} by the reciprocal of \frac{143}{8}.

$$\frac{55}{8}\times \frac{8}{143}$$

Multiply \frac{55}{8} times \frac{8}{143} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55\times 8}{8\times 143}$$

Cancel out 8 in both numerator and denominator.

$$\frac{55}{143}$$

Reduce the fraction \frac{55}{143} to lowest terms by extracting and canceling out 11.

$$\frac{5}{13}$$

Factor

$$\frac{5}{13} = 0.38461538461538464$$