Solve 1/6+1/3+1/2+1/3+frac{1}{2}=

$$\frac { 1 } { 6 } + \frac { 1 } { 3 } + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 2 } =$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

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

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

Since \frac{1}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

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

Add 1 and 2 to get 3.

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

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

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

Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 1 and 1 to get 2.

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

Divide 2 by 2 to get 1.

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

Convert 1 to fraction \frac{3}{3}.

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

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

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

Add 3 and 1 to get 4.

$$\frac{4}{3}+\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{8}{6}+\frac{3}{6}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{8+3}{6}$$

Add 8 and 3 to get 11.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$