Solve 26/7:(5/6-9/14)

$$2 \frac { 6 } { 7 } : ( \frac { 5 } { 6 } - \frac { 9 } { 14 } )$$

Evaluate

$$15$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{14+6}{7}}{\frac{5}{6}-\frac{9}{14}}$$

Add 14 and 6 to get 20.

$$\frac{\frac{20}{7}}{\frac{5}{6}-\frac{9}{14}}$$

Least common multiple of 6 and 14 is 42. Convert \frac{5}{6} and \frac{9}{14} to fractions with denominator 42.

$$\frac{\frac{20}{7}}{\frac{35}{42}-\frac{27}{42}}$$

Since \frac{35}{42} and \frac{27}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20}{7}}{\frac{35-27}{42}}$$

Subtract 27 from 35 to get 8.

$$\frac{\frac{20}{7}}{\frac{8}{42}}$$

Reduce the fraction \frac{8}{42} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{20}{7}}{\frac{4}{21}}$$

Divide \frac{20}{7} by \frac{4}{21} by multiplying \frac{20}{7} by the reciprocal of \frac{4}{21}.

$$\frac{20}{7}\times \frac{21}{4}$$

Multiply \frac{20}{7} times \frac{21}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20\times 21}{7\times 4}$$

Do the multiplications in the fraction \frac{20\times 21}{7\times 4}.

$$\frac{420}{28}$$

Divide 420 by 28 to get 15.

$$15$$

Factor

$$3\times 5$$