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

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

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

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

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

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

$$\frac{\frac{2}{6}+\frac{3}{6}}{\frac{1}{2}-\frac{3}{4}}$$

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

$$\frac{\frac{2+3}{6}}{\frac{1}{2}-\frac{3}{4}}$$

Add 2 and 3 to get 5.

$$\frac{\frac{5}{6}}{\frac{1}{2}-\frac{3}{4}}$$

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

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

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 2 to get -1.

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

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

$$\frac{5}{6}\left(-4\right)$$

Express \frac{5}{6}\left(-4\right) as a single fraction.

$$\frac{5\left(-4\right)}{6}$$

Multiply 5 and -4 to get -20.

$$\frac{-20}{6}$$

Reduce the fraction \frac{-20}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$