Solve 21/3*(-1/2)-2/3*(-2)div1/5]*(-12)

$$2 \frac { 1 } { 3 } \times ( - \frac { 1 } { 2 } ) - \frac { 2 } { 3 } \times ( - 2 ) \div \frac { 1 } { 5 } ] \times ( - 12 )$$

Evaluate

$$\frac{11}{2}=5.5$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{7}{3}\left(-\frac{1}{2}\right)-\frac{\frac{2}{3}\left(-2\right)}{\frac{1}{5}}$$

Multiply \frac{7}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-1\right)}{3\times 2}-\frac{\frac{2}{3}\left(-2\right)}{\frac{1}{5}}$$

Do the multiplications in the fraction \frac{7\left(-1\right)}{3\times 2}.

$$\frac{-7}{6}-\frac{\frac{2}{3}\left(-2\right)}{\frac{1}{5}}$$

Fraction \frac{-7}{6} can be rewritten as -\frac{7}{6} by extracting the negative sign.

$$-\frac{7}{6}-\frac{\frac{2}{3}\left(-2\right)}{\frac{1}{5}}$$

Express \frac{2}{3}\left(-2\right) as a single fraction.

$$-\frac{7}{6}-\frac{\frac{2\left(-2\right)}{3}}{\frac{1}{5}}$$

Multiply 2 and -2 to get -4.

$$-\frac{7}{6}-\frac{\frac{-4}{3}}{\frac{1}{5}}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$-\frac{7}{6}-\frac{-\frac{4}{3}}{\frac{1}{5}}$$

Divide -\frac{4}{3} by \frac{1}{5} by multiplying -\frac{4}{3} by the reciprocal of \frac{1}{5}.

$$-\frac{7}{6}-\left(-\frac{4}{3}\times 5\right)$$

Express -\frac{4}{3}\times 5 as a single fraction.

$$-\frac{7}{6}-\frac{-4\times 5}{3}$$

Multiply -4 and 5 to get -20.

$$-\frac{7}{6}-\frac{-20}{3}$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$-\frac{7}{6}-\left(-\frac{20}{3}\right)$$

The opposite of -\frac{20}{3} is \frac{20}{3}.

$$-\frac{7}{6}+\frac{20}{3}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{7}{6} and \frac{20}{3} to fractions with denominator 6.

$$-\frac{7}{6}+\frac{40}{6}$$

Since -\frac{7}{6} and \frac{40}{6} have the same denominator, add them by adding their numerators.

$$\frac{-7+40}{6}$$

Add -7 and 40 to get 33.

$$\frac{33}{6}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$\frac{11}{2}$$

Factor

$$\frac{11}{2} = 5\frac{1}{2} = 5.5$$