Solve (2-1/3)(-3)+4(-1/2+7/4)=

$$( 2 - \frac { 1 } { 3 } ) ( - 3 ) + 4 ( - \frac { 1 } { 2 } + \frac { 7 } { 4 } ) =$$

Evaluate

$$0$$

Solution Steps

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

$$\left(\frac{6}{3}-\frac{1}{3}\right)\left(-3\right)+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{3}\left(-3\right)+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Subtract 1 from 6 to get 5.

$$\frac{5}{3}\left(-3\right)+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Express \frac{5}{3}\left(-3\right) as a single fraction.

$$\frac{5\left(-3\right)}{3}+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Multiply 5 and -3 to get -15.

$$\frac{-15}{3}+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Divide -15 by 3 to get -5.

$$-5+4\left(-\frac{1}{2}+\frac{7}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{7}{4} to fractions with denominator 4.

$$-5+4\left(-\frac{2}{4}+\frac{7}{4}\right)$$

Since -\frac{2}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$-5+4\times \frac{-2+7}{4}$$

Add -2 and 7 to get 5.

$$-5+4\times \frac{5}{4}$$

Cancel out 4 and 4.

$$-5+5$$

Add -5 and 5 to get 0.

$$0$$

Factor

$$0$$