Solve 2/3+5/6-(-7/2)+7=

$$\frac { 2 } { 3 } + \frac { 5 } { 6 } - ( - \frac { 7 } { 2 } ) + 7 =$$

Evaluate

$$12$$

Solution Steps

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

$$\frac{4}{6}+\frac{5}{6}-\left(-\frac{7}{2}\right)+7$$

Since \frac{4}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{4+5}{6}-\left(-\frac{7}{2}\right)+7$$

Add 4 and 5 to get 9.

$$\frac{9}{6}-\left(-\frac{7}{2}\right)+7$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

The opposite of -\frac{7}{2} is \frac{7}{2}.

$$\frac{3}{2}+\frac{7}{2}+7$$

Since \frac{3}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+7}{2}+7$$

Add 3 and 7 to get 10.

$$\frac{10}{2}+7$$

Divide 10 by 2 to get 5.

$$5+7$$

Add 5 and 7 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$