Solve 1/16-1/8/frac{1{9}-1/18}

$$\frac { \frac { 1 } { 16 } - \frac { 1 } { 8 } } { \frac { 1 } { 9 } - \frac { 1 } { 18 } }$$

Evaluate

$$-\frac{9}{8}=-1.125$$

Solution Steps

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

$$\frac{\frac{1}{16}-\frac{2}{16}}{\frac{1}{9}-\frac{1}{18}}$$

Since \frac{1}{16} and \frac{2}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-2}{16}}{\frac{1}{9}-\frac{1}{18}}$$

Subtract 2 from 1 to get -1.

$$\frac{-\frac{1}{16}}{\frac{1}{9}-\frac{1}{18}}$$

Least common multiple of 9 and 18 is 18. Convert \frac{1}{9} and \frac{1}{18} to fractions with denominator 18.

$$\frac{-\frac{1}{16}}{\frac{2}{18}-\frac{1}{18}}$$

Since \frac{2}{18} and \frac{1}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{16}}{\frac{2-1}{18}}$$

Subtract 1 from 2 to get 1.

$$\frac{-\frac{1}{16}}{\frac{1}{18}}$$

Divide -\frac{1}{16} by \frac{1}{18} by multiplying -\frac{1}{16} by the reciprocal of \frac{1}{18}.

$$-\frac{1}{16}\times 18$$

Express -\frac{1}{16}\times 18 as a single fraction.

$$\frac{-18}{16}$$

Reduce the fraction \frac{-18}{16} to lowest terms by extracting and canceling out 2.

$$-\frac{9}{8}$$

Factor

$$-\frac{9}{8} = -1\frac{1}{8} = -1.125$$