Solve 4/7+(-21/2)+(+1/2)-(-13/7)

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

Evaluate

$$0$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Least common multiple of 7 and 2 is 14. Convert \frac{4}{7} and \frac{5}{2} to fractions with denominator 14.

$$\frac{8}{14}-\frac{35}{14}+\frac{1}{2}-\left(-\frac{1\times 7+3}{7}\right)$$

Since \frac{8}{14} and \frac{35}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-35}{14}+\frac{1}{2}-\left(-\frac{1\times 7+3}{7}\right)$$

Subtract 35 from 8 to get -27.

$$-\frac{27}{14}+\frac{1}{2}-\left(-\frac{1\times 7+3}{7}\right)$$

Least common multiple of 14 and 2 is 14. Convert -\frac{27}{14} and \frac{1}{2} to fractions with denominator 14.

$$-\frac{27}{14}+\frac{7}{14}-\left(-\frac{1\times 7+3}{7}\right)$$

Since -\frac{27}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{-27+7}{14}-\left(-\frac{1\times 7+3}{7}\right)$$

Add -27 and 7 to get -20.

$$\frac{-20}{14}-\left(-\frac{1\times 7+3}{7}\right)$$

Reduce the fraction \frac{-20}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{7}-\left(-\frac{1\times 7+3}{7}\right)$$

Multiply 1 and 7 to get 7.

$$-\frac{10}{7}-\left(-\frac{7+3}{7}\right)$$

Add 7 and 3 to get 10.

$$-\frac{10}{7}-\left(-\frac{10}{7}\right)$$

The opposite of -\frac{10}{7} is \frac{10}{7}.

$$-\frac{10}{7}+\frac{10}{7}$$

Add -\frac{10}{7} and \frac{10}{7} to get 0.

$$0$$

Factor

$$0$$