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

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

Evaluate

$$\frac{15}{2}=7.5$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$\frac{\frac{8}{4}-\frac{3}{4}}{\frac{1}{2}-\frac{1}{3}}$$

Since \frac{8}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-3}{4}}{\frac{1}{2}-\frac{1}{3}}$$

Subtract 3 from 8 to get 5.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{5}{4}}{\frac{3}{6}-\frac{2}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{4}}{\frac{3-2}{6}}$$

Subtract 2 from 3 to get 1.

$$\frac{\frac{5}{4}}{\frac{1}{6}}$$

Divide \frac{5}{4} by \frac{1}{6} by multiplying \frac{5}{4} by the reciprocal of \frac{1}{6}.

$$\frac{5}{4}\times 6$$

Express \frac{5}{4}\times 6 as a single fraction.

$$\frac{5\times 6}{4}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{4}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{15}{2}$$

Factor

$$\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5$$