Solve (5/6-3/4):(1/8+1/2)=

$$( \frac { 5 } { 6 } - \frac { 3 } { 4 } ) : ( \frac { 1 } { 8 } + \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{2}{15}\approx 0.133333333$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\frac{10}{12}-\frac{9}{12}}{\frac{1}{8}+\frac{1}{2}}$$

Since \frac{10}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-9}{12}}{\frac{1}{8}+\frac{1}{2}}$$

Subtract 9 from 10 to get 1.

$$\frac{\frac{1}{12}}{\frac{1}{8}+\frac{1}{2}}$$

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

$$\frac{\frac{1}{12}}{\frac{1}{8}+\frac{4}{8}}$$

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

$$\frac{\frac{1}{12}}{\frac{1+4}{8}}$$

Add 1 and 4 to get 5.

$$\frac{\frac{1}{12}}{\frac{5}{8}}$$

Divide \frac{1}{12} by \frac{5}{8} by multiplying \frac{1}{12} by the reciprocal of \frac{5}{8}.

$$\frac{1}{12}\times \frac{8}{5}$$

Multiply \frac{1}{12} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{12\times 5}$$

Do the multiplications in the fraction \frac{1\times 8}{12\times 5}.

$$\frac{8}{60}$$

Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.

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

Factor

$$\frac{2}{3 \cdot 5} = 0.13333333333333333$$