Solve (1/2+1/3)-(10/5+6/2)

$$( \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } )-( \frac{ 10 }{ 5 } + \frac{ 6 }{ 2 } )$$

Evaluate

$$-\frac{25}{6}\approx -4.166666667$$

Solution Steps

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

$$\frac{3}{6}+\frac{2}{6}-\left(\frac{10}{5}+\frac{6}{2}\right)$$

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

$$\frac{3+2}{6}-\left(\frac{10}{5}+\frac{6}{2}\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{6}-\left(\frac{10}{5}+\frac{6}{2}\right)$$

Divide 10 by 5 to get 2.

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

Divide 6 by 2 to get 3.

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

Add 2 and 3 to get 5.

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

Convert 5 to fraction \frac{30}{6}.

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

Since \frac{5}{6} and \frac{30}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 30 from 5 to get -25.

$$-\frac{25}{6}$$

Factor

$$-\frac{25}{6} = -4\frac{1}{6} = -4.166666666666667$$