Solve 11/14+9/14-(1/2-1/3)

$$\frac { 11 } { 14 } + \frac { 9 } { 14 } - ( \frac { 1 } { 2 } - \frac { 1 } { 3 } )$$

Evaluate

$$\frac{53}{42}\approx 1.261904762$$

Solution Steps

Since \frac{11}{14} and \frac{9}{14} have the same denominator, add them by adding their numerators.

$$\frac{11+9}{14}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Add 11 and 9 to get 20.

$$\frac{20}{14}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Reduce the fraction \frac{20}{14} to lowest terms by extracting and canceling out 2.

$$\frac{10}{7}-\left(\frac{1}{2}-\frac{1}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{10}{7}-\left(\frac{3}{6}-\frac{2}{6}\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{7}-\frac{3-2}{6}$$

Subtract 2 from 3 to get 1.

$$\frac{10}{7}-\frac{1}{6}$$

Least common multiple of 7 and 6 is 42. Convert \frac{10}{7} and \frac{1}{6} to fractions with denominator 42.

$$\frac{60}{42}-\frac{7}{42}$$

Since \frac{60}{42} and \frac{7}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60-7}{42}$$

Subtract 7 from 60 to get 53.

$$\frac{53}{42}$$

Factor

$$\frac{53}{2 \cdot 3 \cdot 7} = 1\frac{11}{42} = 1.2619047619047619$$