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

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

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{8}{12}-\frac{3}{12}}{\frac{3}{2}-\frac{4}{3}}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-3}{12}}{\frac{3}{2}-\frac{4}{3}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{5}{12}}{\frac{3}{2}-\frac{4}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{5}{12}}{\frac{9}{6}-\frac{8}{6}}$$

Since \frac{9}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{9-8}{6}}$$

Subtract 8 from 9 to get 1.

$$\frac{\frac{5}{12}}{\frac{1}{6}}$$

Divide \frac{5}{12} by \frac{1}{6} by multiplying \frac{5}{12} by the reciprocal of \frac{1}{6}.

$$\frac{5}{12}\times 6$$

Express \frac{5}{12}\times 6 as a single fraction.

$$\frac{5\times 6}{12}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{12}$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$