Solve (1/16-1/9+1/12)/(frac{2{7}-frac{1}{6})}

$$\frac { ( \frac { 1 } { 16 } - \frac { 1 } { 9 } + \frac { 1 } { 12 } ) } { ( \frac { 2 } { 7 } - \frac { 1 } { 6 } ) }$$

Evaluate

$$\frac{7}{24}\approx 0.291666667$$

Solution Steps

Least common multiple of 16 and 9 is 144. Convert \frac{1}{16} and \frac{1}{9} to fractions with denominator 144.

$$\frac{\frac{9}{144}-\frac{16}{144}+\frac{1}{12}}{\frac{2}{7}-\frac{1}{6}}$$

Since \frac{9}{144} and \frac{16}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-16}{144}+\frac{1}{12}}{\frac{2}{7}-\frac{1}{6}}$$

Subtract 16 from 9 to get -7.

$$\frac{-\frac{7}{144}+\frac{1}{12}}{\frac{2}{7}-\frac{1}{6}}$$

Least common multiple of 144 and 12 is 144. Convert -\frac{7}{144} and \frac{1}{12} to fractions with denominator 144.

$$\frac{-\frac{7}{144}+\frac{12}{144}}{\frac{2}{7}-\frac{1}{6}}$$

Since -\frac{7}{144} and \frac{12}{144} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-7+12}{144}}{\frac{2}{7}-\frac{1}{6}}$$

Add -7 and 12 to get 5.

$$\frac{\frac{5}{144}}{\frac{2}{7}-\frac{1}{6}}$$

Least common multiple of 7 and 6 is 42. Convert \frac{2}{7} and \frac{1}{6} to fractions with denominator 42.

$$\frac{\frac{5}{144}}{\frac{12}{42}-\frac{7}{42}}$$

Since \frac{12}{42} and \frac{7}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{144}}{\frac{12-7}{42}}$$

Subtract 7 from 12 to get 5.

$$\frac{\frac{5}{144}}{\frac{5}{42}}$$

Divide \frac{5}{144} by \frac{5}{42} by multiplying \frac{5}{144} by the reciprocal of \frac{5}{42}.

$$\frac{5}{144}\times \frac{42}{5}$$

Multiply \frac{5}{144} times \frac{42}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 42}{144\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{42}{144}$$

Reduce the fraction \frac{42}{144} to lowest terms by extracting and canceling out 6.

$$\frac{7}{24}$$

Factor

$$\frac{7}{2 ^ {3} \cdot 3} = 0.2916666666666667$$