Solve (1/3*8/1-1/2*4/1-2*2)-(-frac{1}{3}-frac{1}{2}+2)

$$( \frac { 1 } { 3 } \times \frac { 8 } { 1 } - \frac { 1 } { 2 } \times \frac { 4 } { 1 } - 2 \times 2 ) - ( - \frac { 1 } { 3 } - \frac { 1 } { 2 } + 2 )$$

Evaluate

$$-\frac{9}{2}=-4.5$$

Solution Steps

Anything divided by one gives itself.

$$\frac{1}{3}\times 8-\frac{1}{2}\times \frac{4}{1}-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Multiply \frac{1}{3} and 8 to get \frac{8}{3}.

$$\frac{8}{3}-\frac{1}{2}\times \frac{4}{1}-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Anything divided by one gives itself.

$$\frac{8}{3}-\frac{1}{2}\times 4-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{8}{3}-\frac{4}{2}-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Divide 4 by 2 to get 2.

$$\frac{8}{3}-2-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

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

$$\frac{8}{3}-\frac{6}{3}-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Since \frac{8}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-6}{3}-2\times 2-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Subtract 6 from 8 to get 2.

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

Multiply 2 and 2 to get 4.

$$\frac{2}{3}-4-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{2}{3}-\frac{12}{3}-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Since \frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-12}{3}-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

Subtract 12 from 2 to get -10.

$$-\frac{10}{3}-\left(-\frac{1}{3}-\frac{1}{2}+2\right)$$

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

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

Since -\frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -2 to get -5.

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

Convert 2 to fraction \frac{12}{6}.

$$-\frac{10}{3}-\left(-\frac{5}{6}+\frac{12}{6}\right)$$

Since -\frac{5}{6} and \frac{12}{6} have the same denominator, add them by adding their numerators.

$$-\frac{10}{3}-\frac{-5+12}{6}$$

Add -5 and 12 to get 7.

$$-\frac{10}{3}-\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{10}{3} and \frac{7}{6} to fractions with denominator 6.

$$-\frac{20}{6}-\frac{7}{6}$$

Since -\frac{20}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-7}{6}$$

Subtract 7 from -20 to get -27.

$$\frac{-27}{6}$$

Reduce the fraction \frac{-27}{6} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{2}$$

Factor

$$-\frac{9}{2} = -4\frac{1}{2} = -4.5$$