Solve 9/10-(1/6+2/5)

$$\frac { 9 } { 10 } - ( \frac { 1 } { 6 } + \frac { 2 } { 5 } )$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{2}{5} to fractions with denominator 30.

$$\frac{9}{10}-\left(\frac{5}{30}+\frac{12}{30}\right)$$

Since \frac{5}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$\frac{9}{10}-\frac{5+12}{30}$$

Add 5 and 12 to get 17.

$$\frac{9}{10}-\frac{17}{30}$$

Least common multiple of 10 and 30 is 30. Convert \frac{9}{10} and \frac{17}{30} to fractions with denominator 30.

$$\frac{27}{30}-\frac{17}{30}$$

Since \frac{27}{30} and \frac{17}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-17}{30}$$

Subtract 17 from 27 to get 10.

$$\frac{10}{30}$$

Reduce the fraction \frac{10}{30} to lowest terms by extracting and canceling out 10.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$