Solve 7/12:(1/4-2/9)

$$\frac { 7 } { 12 } : ( \frac { 1 } { 4 } - \frac { 2 } { 9 } )$$

Evaluate

$$21$$

Solution Steps

Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{2}{9} to fractions with denominator 36.

$$\frac{\frac{7}{12}}{\frac{9}{36}-\frac{8}{36}}$$

Since \frac{9}{36} and \frac{8}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{12}}{\frac{9-8}{36}}$$

Subtract 8 from 9 to get 1.

$$\frac{\frac{7}{12}}{\frac{1}{36}}$$

Divide \frac{7}{12} by \frac{1}{36} by multiplying \frac{7}{12} by the reciprocal of \frac{1}{36}.

$$\frac{7}{12}\times 36$$

Express \frac{7}{12}\times 36 as a single fraction.

$$\frac{7\times 36}{12}$$

Multiply 7 and 36 to get 252.

$$\frac{252}{12}$$

Divide 252 by 12 to get 21.

$$21$$

Factor

$$3\times 7$$