Solve 1/2-1/8/frac{1{5}+1/4}

$$\frac { \frac { 1 } { 2 } - \frac { 1 } { 8 } } { \frac { 1 } { 5 } + \frac { 1 } { 4 } }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{1}{8} to fractions with denominator 8.

$$\frac{\frac{4}{8}-\frac{1}{8}}{\frac{1}{5}+\frac{1}{4}}$$

Since \frac{4}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{8}}{\frac{1}{5}+\frac{1}{4}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{8}}{\frac{1}{5}+\frac{1}{4}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{1}{4} to fractions with denominator 20.

$$\frac{\frac{3}{8}}{\frac{4}{20}+\frac{5}{20}}$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{8}}{\frac{4+5}{20}}$$

Add 4 and 5 to get 9.

$$\frac{\frac{3}{8}}{\frac{9}{20}}$$

Divide \frac{3}{8} by \frac{9}{20} by multiplying \frac{3}{8} by the reciprocal of \frac{9}{20}.

$$\frac{3}{8}\times \frac{20}{9}$$

Multiply \frac{3}{8} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 20}{8\times 9}$$

Do the multiplications in the fraction \frac{3\times 20}{8\times 9}.

$$\frac{60}{72}$$

Reduce the fraction \frac{60}{72} to lowest terms by extracting and canceling out 12.

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

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$