Solve 1/2+1/3+1/6/2-frac{5{3}}

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

Evaluate

$$3$$

Solution Steps

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

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Since \frac{5}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

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

Add 5 and 1 to get 6.

$$\frac{\frac{6}{6}}{2-\frac{5}{3}}$$

Divide 6 by 6 to get 1.

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

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

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

Since \frac{6}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 6 to get 1.

$$\frac{1}{\frac{1}{3}}$$

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

$$1\times 3$$

Multiply 1 and 3 to get 3.

$$3$$

Factor

$$3$$