Solve 7/6-(3/5-1/6)

$$\frac { 7 } { 6 } - ( \frac { 3 } { 5 } - \frac { 1 } { 6 } )$$

Evaluate

$$\frac{11}{15}\approx 0.733333333$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{3}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{7}{6}-\left(\frac{18}{30}-\frac{5}{30}\right)$$

Since \frac{18}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}-\frac{18-5}{30}$$

Subtract 5 from 18 to get 13.

$$\frac{7}{6}-\frac{13}{30}$$

Least common multiple of 6 and 30 is 30. Convert \frac{7}{6} and \frac{13}{30} to fractions with denominator 30.

$$\frac{35}{30}-\frac{13}{30}$$

Since \frac{35}{30} and \frac{13}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-13}{30}$$

Subtract 13 from 35 to get 22.

$$\frac{22}{30}$$

Reduce the fraction \frac{22}{30} to lowest terms by extracting and canceling out 2.

$$\frac{11}{15}$$

Factor

$$\frac{11}{3 \cdot 5} = 0.7333333333333333$$