Solve (-2/5-1/2):(4/5-3/4)=

$$( - \frac { 2 } { 5 } - \frac { 1 } { 2 } ) : ( \frac { 4 } { 5 } - \frac { 3 } { 4 } ) =$$

Evaluate

$$-18$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert -\frac{2}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{-\frac{4}{10}-\frac{5}{10}}{\frac{4}{5}-\frac{3}{4}}$$

Since -\frac{4}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-4-5}{10}}{\frac{4}{5}-\frac{3}{4}}$$

Subtract 5 from -4 to get -9.

$$\frac{-\frac{9}{10}}{\frac{4}{5}-\frac{3}{4}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{4}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{-\frac{9}{10}}{\frac{16}{20}-\frac{15}{20}}$$

Since \frac{16}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{9}{10}}{\frac{16-15}{20}}$$

Subtract 15 from 16 to get 1.

$$\frac{-\frac{9}{10}}{\frac{1}{20}}$$

Divide -\frac{9}{10} by \frac{1}{20} by multiplying -\frac{9}{10} by the reciprocal of \frac{1}{20}.

$$-\frac{9}{10}\times 20$$

Express -\frac{9}{10}\times 20 as a single fraction.

$$\frac{-9\times 20}{10}$$

Multiply -9 and 20 to get -180.

$$\frac{-180}{10}$$

Divide -180 by 10 to get -18.

$$-18$$

Factor

$$-18$$