Solve 1/2+2/3+3/2/frac{1{3}-frac{2}{3}+frac{5}{3}}

$$\frac { \frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 2 } } { \frac { 1 } { 3 } - \frac { 2 } { 3 } + \frac { 5 } { 3 } }$$

Evaluate

$$2$$

Solution Steps

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

$$\frac{\frac{3}{6}+\frac{4}{6}+\frac{3}{2}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+4}{6}+\frac{3}{2}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{7}{6}+\frac{3}{2}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Least common multiple of 6 and 2 is 6. Convert \frac{7}{6} and \frac{3}{2} to fractions with denominator 6.

$$\frac{\frac{7}{6}+\frac{9}{6}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Since \frac{7}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7+9}{6}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Add 7 and 9 to get 16.

$$\frac{\frac{16}{6}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{8}{3}}{\frac{1}{3}-\frac{2}{3}+\frac{5}{3}}$$

Since \frac{1}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8}{3}}{\frac{1-2}{3}+\frac{5}{3}}$$

Subtract 2 from 1 to get -1.

$$\frac{\frac{8}{3}}{-\frac{1}{3}+\frac{5}{3}}$$

Since -\frac{1}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{3}}{\frac{-1+5}{3}}$$

Add -1 and 5 to get 4.

$$\frac{\frac{8}{3}}{\frac{4}{3}}$$

Divide \frac{8}{3} by \frac{4}{3} by multiplying \frac{8}{3} by the reciprocal of \frac{4}{3}.

$$\frac{8}{3}\times \frac{3}{4}$$

Multiply \frac{8}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 3}{3\times 4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$2$$

Factor

$$2$$