Solve (5/16+1/8)div(5/4-1/12)

$$( \frac { 5 } { 16 } + \frac { 1 } { 8 } ) \div ( \frac { 5 } { 4 } - \frac { 1 } { 12 } )$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

Least common multiple of 16 and 8 is 16. Convert \frac{5}{16} and \frac{1}{8} to fractions with denominator 16.

$$\frac{\frac{5}{16}+\frac{2}{16}}{\frac{5}{4}-\frac{1}{12}}$$

Since \frac{5}{16} and \frac{2}{16} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+2}{16}}{\frac{5}{4}-\frac{1}{12}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{7}{16}}{\frac{5}{4}-\frac{1}{12}}$$

Least common multiple of 4 and 12 is 12. Convert \frac{5}{4} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{7}{16}}{\frac{15}{12}-\frac{1}{12}}$$

Since \frac{15}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{16}}{\frac{15-1}{12}}$$

Subtract 1 from 15 to get 14.

$$\frac{\frac{7}{16}}{\frac{14}{12}}$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{16}}{\frac{7}{6}}$$

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

$$\frac{7}{16}\times \frac{6}{7}$$

Multiply \frac{7}{16} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 6}{16\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{6}{16}$$

Reduce the fraction \frac{6}{16} to lowest terms by extracting and canceling out 2.

$$\frac{3}{8}$$

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$