Solve 5/6-(1/5+7/15)

$$\frac { 5 } { 6 } - ( \frac { 1 } { 5 } + \frac { 7 } { 15 } )$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{7}{15} to fractions with denominator 15.

$$\frac{5}{6}-\left(\frac{3}{15}+\frac{7}{15}\right)$$

Since \frac{3}{15} and \frac{7}{15} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}-\frac{3+7}{15}$$

Add 3 and 7 to get 10.

$$\frac{5}{6}-\frac{10}{15}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

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

Since \frac{5}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 5 to get 1.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$