Solve 11/13div(5/8+3/4)div3/8

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

Evaluate

$$\frac{64}{39}\approx 1.641025641$$

Solution Steps

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

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

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

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

Multiply 11 and 8 to get 88.

$$\frac{\frac{88}{13}}{\left(\frac{5}{8}+\frac{3}{4}\right)\times 3}$$

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

$$\frac{\frac{88}{13}}{\left(\frac{5}{8}+\frac{6}{8}\right)\times 3}$$

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

$$\frac{\frac{88}{13}}{\frac{5+6}{8}\times 3}$$

Add 5 and 6 to get 11.

$$\frac{\frac{88}{13}}{\frac{11}{8}\times 3}$$

Express \frac{11}{8}\times 3 as a single fraction.

$$\frac{\frac{88}{13}}{\frac{11\times 3}{8}}$$

Multiply 11 and 3 to get 33.

$$\frac{\frac{88}{13}}{\frac{33}{8}}$$

Divide \frac{88}{13} by \frac{33}{8} by multiplying \frac{88}{13} by the reciprocal of \frac{33}{8}.

$$\frac{88}{13}\times \frac{8}{33}$$

Multiply \frac{88}{13} times \frac{8}{33} by multiplying numerator times numerator and denominator times denominator.

$$\frac{88\times 8}{13\times 33}$$

Do the multiplications in the fraction \frac{88\times 8}{13\times 33}.

$$\frac{704}{429}$$

Reduce the fraction \frac{704}{429} to lowest terms by extracting and canceling out 11.

$$\frac{64}{39}$$

Factor

$$\frac{2 ^ {6}}{3 \cdot 13} = 1\frac{25}{39} = 1.641025641025641$$