Solve 7/9div[(5/8-1/4)*12]

$$\frac { 7 } { 9 } \div [ ( \frac { 5 } { 8 } - \frac { 1 } { 4 } ) \times 12 ]$$

Evaluate

$$\frac{14}{81}\approx 0.172839506$$

Solution Steps

Least common multiple of 8 and 4 is 8. Convert \frac{5}{8} and \frac{1}{4} to fractions with denominator 8.

$$\frac{\frac{7}{9}}{\left(\frac{5}{8}-\frac{2}{8}\right)\times 12}$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{9}}{\frac{5-2}{8}\times 12}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{7}{9}}{\frac{3}{8}\times 12}$$

Express \frac{3}{8}\times 12 as a single fraction.

$$\frac{\frac{7}{9}}{\frac{3\times 12}{8}}$$

Multiply 3 and 12 to get 36.

$$\frac{\frac{7}{9}}{\frac{36}{8}}$$

Reduce the fraction \frac{36}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{9}}{\frac{9}{2}}$$

Divide \frac{7}{9} by \frac{9}{2} by multiplying \frac{7}{9} by the reciprocal of \frac{9}{2}.

$$\frac{7}{9}\times \frac{2}{9}$$

Multiply \frac{7}{9} times \frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2}{9\times 9}$$

Do the multiplications in the fraction \frac{7\times 2}{9\times 9}.

$$\frac{14}{81}$$

Factor

$$\frac{2 \cdot 7}{3 ^ {4}} = 0.1728395061728395$$