Solve 1/2+1/3+1/6+1/9+frac{1}{18}

$$\frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 6 } + \frac { 1 } { 9 } + \frac { 1 } { 18 }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

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

$$\frac{3}{6}+\frac{2}{6}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

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

$$\frac{3+2}{6}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Add 3 and 2 to get 5.

$$\frac{5}{6}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

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

$$\frac{5+1}{6}+\frac{1}{9}+\frac{1}{18}$$

Add 5 and 1 to get 6.

$$\frac{6}{6}+\frac{1}{9}+\frac{1}{18}$$

Divide 6 by 6 to get 1.

$$1+\frac{1}{9}+\frac{1}{18}$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{9}{9}+\frac{1}{9}+\frac{1}{18}$$

Since \frac{9}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{9}+\frac{1}{18}$$

Add 9 and 1 to get 10.

$$\frac{10}{9}+\frac{1}{18}$$

Least common multiple of 9 and 18 is 18. Convert \frac{10}{9} and \frac{1}{18} to fractions with denominator 18.

$$\frac{20}{18}+\frac{1}{18}$$

Since \frac{20}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{20+1}{18}$$

Add 20 and 1 to get 21.

$$\frac{21}{18}$$

Reduce the fraction \frac{21}{18} to lowest terms by extracting and canceling out 3.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$