Solve -3/2+8/7+1/2-3=

$$- \frac { 3 } { 2 } + \frac { 8 } { 7 } + \frac { 1 } { 2 } - 3 =$$

Evaluate

$$-\frac{20}{7}\approx -2.857142857$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert -\frac{3}{2} and \frac{8}{7} to fractions with denominator 14.

$$-\frac{21}{14}+\frac{16}{14}+\frac{1}{2}-3$$

Since -\frac{21}{14} and \frac{16}{14} have the same denominator, add them by adding their numerators.

$$\frac{-21+16}{14}+\frac{1}{2}-3$$

Add -21 and 16 to get -5.

$$-\frac{5}{14}+\frac{1}{2}-3$$

Least common multiple of 14 and 2 is 14. Convert -\frac{5}{14} and \frac{1}{2} to fractions with denominator 14.

$$-\frac{5}{14}+\frac{7}{14}-3$$

Since -\frac{5}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{-5+7}{14}-3$$

Add -5 and 7 to get 2.

$$\frac{2}{14}-3$$

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

$$\frac{1}{7}-3$$

Convert 3 to fraction \frac{21}{7}.

$$\frac{1}{7}-\frac{21}{7}$$

Since \frac{1}{7} and \frac{21}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-21}{7}$$

Subtract 21 from 1 to get -20.

$$-\frac{20}{7}$$

Factor

$$-\frac{20}{7} = -2\frac{6}{7} = -2.857142857142857$$