Solve (1/2+1/3)div(1-3/8)

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) \div ( 1 - \frac { 3 } { 8 } )$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

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

$$\frac{\frac{3}{6}+\frac{2}{6}}{1-\frac{3}{8}}$$

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

$$\frac{\frac{3+2}{6}}{1-\frac{3}{8}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{5}{6}}{1-\frac{3}{8}}$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{\frac{5}{6}}{\frac{8}{8}-\frac{3}{8}}$$

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

$$\frac{\frac{5}{6}}{\frac{8-3}{8}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{5}{6}}{\frac{5}{8}}$$

Divide \frac{5}{6} by \frac{5}{8} by multiplying \frac{5}{6} by the reciprocal of \frac{5}{8}.

$$\frac{5}{6}\times \frac{8}{5}$$

Multiply \frac{5}{6} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 8}{6\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$