Solve 3/5-2/3/frac{1{3}-1/4}

$$\frac { \frac { 3 } { 5 } - \frac { 2 } { 3 } } { \frac { 1 } { 3 } - \frac { 1 } { 4 } }$$

Evaluate

$$-\frac{4}{5}=-0.8$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{\frac{9}{15}-\frac{10}{15}}{\frac{1}{3}-\frac{1}{4}}$$

Since \frac{9}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-10}{15}}{\frac{1}{3}-\frac{1}{4}}$$

Subtract 10 from 9 to get -1.

$$\frac{-\frac{1}{15}}{\frac{1}{3}-\frac{1}{4}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{-\frac{1}{15}}{\frac{4}{12}-\frac{3}{12}}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{1}{15}}{\frac{4-3}{12}}$$

Subtract 3 from 4 to get 1.

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

Divide -\frac{1}{15} by \frac{1}{12} by multiplying -\frac{1}{15} by the reciprocal of \frac{1}{12}.

$$-\frac{1}{15}\times 12$$

Express -\frac{1}{15}\times 12 as a single fraction.

$$\frac{-12}{15}$$

Reduce the fraction \frac{-12}{15} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{4}{5} = -0.8$$