Solve 5/7div8/7+7/8div7/5-frac{5}{7}

$$\frac { 5 } { 7 } \div \frac { 8 } { 7 } + \frac { 7 } { 8 } \div \frac { 7 } { 5 } - \frac { 5 } { 7 }$$

Evaluate

$$\frac{15}{28}\approx 0.535714286$$

Solution Steps

Divide \frac{5}{7} by \frac{8}{7} by multiplying \frac{5}{7} by the reciprocal of \frac{8}{7}.

$$\frac{5}{7}\times \frac{7}{8}+\frac{\frac{7}{8}}{\frac{7}{5}}-\frac{5}{7}$$

Multiply \frac{5}{7} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 7}{7\times 8}+\frac{\frac{7}{8}}{\frac{7}{5}}-\frac{5}{7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{5}{8}+\frac{\frac{7}{8}}{\frac{7}{5}}-\frac{5}{7}$$

Divide \frac{7}{8} by \frac{7}{5} by multiplying \frac{7}{8} by the reciprocal of \frac{7}{5}.

$$\frac{5}{8}+\frac{7}{8}\times \frac{5}{7}-\frac{5}{7}$$

Multiply \frac{7}{8} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}+\frac{7\times 5}{8\times 7}-\frac{5}{7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{5}{8}+\frac{5}{8}-\frac{5}{7}$$

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

$$\frac{5+5}{8}-\frac{5}{7}$$

Add 5 and 5 to get 10.

$$\frac{10}{8}-\frac{5}{7}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}-\frac{5}{7}$$

Least common multiple of 4 and 7 is 28. Convert \frac{5}{4} and \frac{5}{7} to fractions with denominator 28.

$$\frac{35}{28}-\frac{20}{28}$$

Since \frac{35}{28} and \frac{20}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-20}{28}$$

Subtract 20 from 35 to get 15.

$$\frac{15}{28}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {2} \cdot 7} = 0.5357142857142857$$