Solve (7/9div7/10)div5/6

$$( \frac { 7 } { 9 } \div \frac { 7 } { 10 } ) \div \frac { 5 } { 6 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Divide \frac{\frac{7}{9}}{\frac{7}{10}} by \frac{5}{6} by multiplying \frac{\frac{7}{9}}{\frac{7}{10}} by the reciprocal of \frac{5}{6}.

$$\frac{\frac{7}{9}\times 6}{\frac{7}{10}\times 5}$$

Express \frac{7}{9}\times 6 as a single fraction.

$$\frac{\frac{7\times 6}{9}}{\frac{7}{10}\times 5}$$

Multiply 7 and 6 to get 42.

$$\frac{\frac{42}{9}}{\frac{7}{10}\times 5}$$

Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{14}{3}}{\frac{7}{10}\times 5}$$

Express \frac{7}{10}\times 5 as a single fraction.

$$\frac{\frac{14}{3}}{\frac{7\times 5}{10}}$$

Multiply 7 and 5 to get 35.

$$\frac{\frac{14}{3}}{\frac{35}{10}}$$

Reduce the fraction \frac{35}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{14}{3}}{\frac{7}{2}}$$

Divide \frac{14}{3} by \frac{7}{2} by multiplying \frac{14}{3} by the reciprocal of \frac{7}{2}.

$$\frac{14}{3}\times \frac{2}{7}$$

Multiply \frac{14}{3} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 2}{3\times 7}$$

Do the multiplications in the fraction \frac{14\times 2}{3\times 7}.

$$\frac{28}{21}$$

Reduce the fraction \frac{28}{21} to lowest terms by extracting and canceling out 7.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$