Solve 1/10-(3/5-1/3)

$$\frac { 1 } { 10 } - ( \frac { 3 } { 5 } - \frac { 1 } { 3 } )$$

Evaluate

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

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{1}{10}-\left(\frac{9}{15}-\frac{5}{15}\right)$$

Since \frac{9}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{10}-\frac{9-5}{15}$$

Subtract 5 from 9 to get 4.

$$\frac{1}{10}-\frac{4}{15}$$

Least common multiple of 10 and 15 is 30. Convert \frac{1}{10} and \frac{4}{15} to fractions with denominator 30.

$$\frac{3}{30}-\frac{8}{30}$$

Since \frac{3}{30} and \frac{8}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{30}$$

Subtract 8 from 3 to get -5.

$$\frac{-5}{30}$$

Reduce the fraction \frac{-5}{30} to lowest terms by extracting and canceling out 5.

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

Factor

$$-\frac{1}{6} = -0.16666666666666666$$