Solve 6/7div(5/6-4/5)div7/16]

$$\frac { 6 } { 7 } \div ( \frac { 5 } { 6 } - \frac { 4 } { 5 } ) \div \frac { 7 } { 16 } ]$$

Evaluate

$$\frac{2880}{49}\approx 58.775510204$$

Solution Steps

Divide \frac{\frac{6}{7}}{\frac{5}{6}-\frac{4}{5}} by \frac{7}{16} by multiplying \frac{\frac{6}{7}}{\frac{5}{6}-\frac{4}{5}} by the reciprocal of \frac{7}{16}.

$$\frac{\frac{6}{7}\times 16}{\left(\frac{5}{6}-\frac{4}{5}\right)\times 7}$$

Express \frac{6}{7}\times 16 as a single fraction.

$$\frac{\frac{6\times 16}{7}}{\left(\frac{5}{6}-\frac{4}{5}\right)\times 7}$$

Multiply 6 and 16 to get 96.

$$\frac{\frac{96}{7}}{\left(\frac{5}{6}-\frac{4}{5}\right)\times 7}$$

Least common multiple of 6 and 5 is 30. Convert \frac{5}{6} and \frac{4}{5} to fractions with denominator 30.

$$\frac{\frac{96}{7}}{\left(\frac{25}{30}-\frac{24}{30}\right)\times 7}$$

Since \frac{25}{30} and \frac{24}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{96}{7}}{\frac{25-24}{30}\times 7}$$

Subtract 24 from 25 to get 1.

$$\frac{\frac{96}{7}}{\frac{1}{30}\times 7}$$

Multiply \frac{1}{30} and 7 to get \frac{7}{30}.

$$\frac{\frac{96}{7}}{\frac{7}{30}}$$

Divide \frac{96}{7} by \frac{7}{30} by multiplying \frac{96}{7} by the reciprocal of \frac{7}{30}.

$$\frac{96}{7}\times \frac{30}{7}$$

Multiply \frac{96}{7} times \frac{30}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{96\times 30}{7\times 7}$$

Do the multiplications in the fraction \frac{96\times 30}{7\times 7}.

$$\frac{2880}{49}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {2} \cdot 5}{7 ^ {2}} = 58\frac{38}{49} = 58.775510204081634$$