Solve 4/5+1/2-(2/5-2/7)

$$\frac { 4 } { 5 } + \frac { 1 } { 2 } - ( \frac { 2 } { 5 } - \frac { 2 } { 7 } )$$

Evaluate

$$\frac{83}{70}\approx 1.185714286$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{8}{10}+\frac{5}{10}-\left(\frac{2}{5}-\frac{2}{7}\right)$$

Since \frac{8}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{8+5}{10}-\left(\frac{2}{5}-\frac{2}{7}\right)$$

Add 8 and 5 to get 13.

$$\frac{13}{10}-\left(\frac{2}{5}-\frac{2}{7}\right)$$

Least common multiple of 5 and 7 is 35. Convert \frac{2}{5} and \frac{2}{7} to fractions with denominator 35.

$$\frac{13}{10}-\left(\frac{14}{35}-\frac{10}{35}\right)$$

Since \frac{14}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{10}-\frac{14-10}{35}$$

Subtract 10 from 14 to get 4.

$$\frac{13}{10}-\frac{4}{35}$$

Least common multiple of 10 and 35 is 70. Convert \frac{13}{10} and \frac{4}{35} to fractions with denominator 70.

$$\frac{91}{70}-\frac{8}{70}$$

Since \frac{91}{70} and \frac{8}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-8}{70}$$

Subtract 8 from 91 to get 83.

$$\frac{83}{70}$$

Factor

$$\frac{83}{2 \cdot 5 \cdot 7} = 1\frac{13}{70} = 1.1857142857142857$$