Solve (-12/3)-(-1/2)-2.5+(-31/3)

$$( - 1 \frac { 2 } { 3 } ) - ( - \frac { 1 } { 2 } ) - 2.5 + ( - 3 \frac { 1 } { 3 } )$$

Evaluate

$$-7$$

Solution Steps

Multiply 1 and 3 to get 3.

$$-\frac{3+2}{3}-\left(-\frac{1}{2}\right)-2.5-\frac{3\times 3+1}{3}$$

Add 3 and 2 to get 5.

$$-\frac{5}{3}-\left(-\frac{1}{2}\right)-2.5-\frac{3\times 3+1}{3}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$-\frac{5}{3}+\frac{1}{2}-2.5-\frac{3\times 3+1}{3}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{5}{3} and \frac{1}{2} to fractions with denominator 6.

$$-\frac{10}{6}+\frac{3}{6}-2.5-\frac{3\times 3+1}{3}$$

Since -\frac{10}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{-10+3}{6}-2.5-\frac{3\times 3+1}{3}$$

Add -10 and 3 to get -7.

$$-\frac{7}{6}-2.5-\frac{3\times 3+1}{3}$$

Convert decimal number 2.5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{7}{6}-\frac{5}{2}-\frac{3\times 3+1}{3}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{7}{6} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{7}{6}-\frac{15}{6}-\frac{3\times 3+1}{3}$$

Since -\frac{7}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-15}{6}-\frac{3\times 3+1}{3}$$

Subtract 15 from -7 to get -22.

$$\frac{-22}{6}-\frac{3\times 3+1}{3}$$

Reduce the fraction \frac{-22}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{3}-\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{11}{3}-\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$-\frac{11}{3}-\frac{10}{3}$$

Since -\frac{11}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-10}{3}$$

Subtract 10 from -11 to get -21.

$$\frac{-21}{3}$$

Divide -21 by 3 to get -7.

$$-7$$

Factor

$$-7$$