Solve (7/8-3/5)div1/8*(1/5+frac{1}{2})

$$( \frac { 7 } { 8 } - \frac { 3 } { 5 } ) \div \frac { 1 } { 8 } \times ( \frac { 1 } { 5 } + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{77}{50}=1.54$$

Solution Steps

Least common multiple of 8 and 5 is 40. Convert \frac{7}{8} and \frac{3}{5} to fractions with denominator 40.

$$\frac{\frac{35}{40}-\frac{24}{40}}{\frac{1}{8}}\left(\frac{1}{5}+\frac{1}{2}\right)$$

Since \frac{35}{40} and \frac{24}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{35-24}{40}}{\frac{1}{8}}\left(\frac{1}{5}+\frac{1}{2}\right)$$

Subtract 24 from 35 to get 11.

$$\frac{\frac{11}{40}}{\frac{1}{8}}\left(\frac{1}{5}+\frac{1}{2}\right)$$

Divide \frac{11}{40} by \frac{1}{8} by multiplying \frac{11}{40} by the reciprocal of \frac{1}{8}.

$$\frac{11}{40}\times 8\left(\frac{1}{5}+\frac{1}{2}\right)$$

Express \frac{11}{40}\times 8 as a single fraction.

$$\frac{11\times 8}{40}\left(\frac{1}{5}+\frac{1}{2}\right)$$

Multiply 11 and 8 to get 88.

$$\frac{88}{40}\left(\frac{1}{5}+\frac{1}{2}\right)$$

Reduce the fraction \frac{88}{40} to lowest terms by extracting and canceling out 8.

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

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{11}{5}\left(\frac{2}{10}+\frac{5}{10}\right)$$

Since \frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{11}{5}\times \frac{2+5}{10}$$

Add 2 and 5 to get 7.

$$\frac{11}{5}\times \frac{7}{10}$$

Multiply \frac{11}{5} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 7}{5\times 10}$$

Do the multiplications in the fraction \frac{11\times 7}{5\times 10}.

$$\frac{77}{50}$$

Factor

$$\frac{7 \cdot 11}{2 \cdot 5 ^ {2}} = 1\frac{27}{50} = 1.54$$