Solve (1/2+1/3)-(1/5+5/7)

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) - ( \frac { 1 } { 5 } + \frac { 5 } { 7 } )$$

Evaluate

$$-\frac{17}{210}\approx -0.080952381$$

Solution Steps

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

$$\frac{3}{6}+\frac{2}{6}-\left(\frac{1}{5}+\frac{5}{7}\right)$$

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

$$\frac{3+2}{6}-\left(\frac{1}{5}+\frac{5}{7}\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{6}-\left(\frac{1}{5}+\frac{5}{7}\right)$$

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{5}{7} to fractions with denominator 35.

$$\frac{5}{6}-\left(\frac{7}{35}+\frac{25}{35}\right)$$

Since \frac{7}{35} and \frac{25}{35} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}-\frac{7+25}{35}$$

Add 7 and 25 to get 32.

$$\frac{5}{6}-\frac{32}{35}$$

Least common multiple of 6 and 35 is 210. Convert \frac{5}{6} and \frac{32}{35} to fractions with denominator 210.

$$\frac{175}{210}-\frac{192}{210}$$

Since \frac{175}{210} and \frac{192}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{175-192}{210}$$

Subtract 192 from 175 to get -17.

$$-\frac{17}{210}$$

Factor

$$-\frac{17}{210} = -0.08095238095238096$$