Solve 3-1/2-(-2)/3-23/2

$$3 - \frac { 1 } { 2 } - \frac { ( - 2 ) } { 3 } - 2 \frac { 3 } { 2 }$$

Evaluate

$$-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Convert 3 to fraction \frac{6}{2}.

$$\frac{6}{2}-\frac{1}{2}-\frac{-2}{3}-\frac{2\times 2+3}{2}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{2}-\frac{-2}{3}-\frac{2\times 2+3}{2}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{2}-\frac{-2}{3}-\frac{2\times 2+3}{2}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\frac{5}{2}+\frac{2}{3}-\frac{2\times 2+3}{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{15}{6}+\frac{4}{6}-\frac{2\times 2+3}{2}$$

Since \frac{15}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+4}{6}-\frac{2\times 2+3}{2}$$

Add 15 and 4 to get 19.

$$\frac{19}{6}-\frac{2\times 2+3}{2}$$

Multiply 2 and 2 to get 4.

$$\frac{19}{6}-\frac{4+3}{2}$$

Add 4 and 3 to get 7.

$$\frac{19}{6}-\frac{7}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{19}{6} and \frac{7}{2} to fractions with denominator 6.

$$\frac{19}{6}-\frac{21}{6}$$

Since \frac{19}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-21}{6}$$

Subtract 21 from 19 to get -2.

$$\frac{-2}{6}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{1}{3} = -0.3333333333333333$$