Solve 1/12+1/18+1/6+1/36+frac{1}{6}+frac{1}{9}+frac{1}{18}

$$\frac { 1 } { 12 } + \frac { 1 } { 18 } + \frac { 1 } { 6 } + \frac { 1 } { 36 } + \frac { 1 } { 6 } + \frac { 1 } { 9 } + \frac { 1 } { 18 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Least common multiple of 12 and 18 is 36. Convert \frac{1}{12} and \frac{1}{18} to fractions with denominator 36.

$$\frac{3}{36}+\frac{2}{36}+\frac{1}{6}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Since \frac{3}{36} and \frac{2}{36} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{36}+\frac{1}{6}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Add 3 and 2 to get 5.

$$\frac{5}{36}+\frac{1}{6}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Least common multiple of 36 and 6 is 36. Convert \frac{5}{36} and \frac{1}{6} to fractions with denominator 36.

$$\frac{5}{36}+\frac{6}{36}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Since \frac{5}{36} and \frac{6}{36} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{36}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Add 5 and 6 to get 11.

$$\frac{11}{36}+\frac{1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Since \frac{11}{36} and \frac{1}{36} have the same denominator, add them by adding their numerators.

$$\frac{11+1}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Add 11 and 1 to get 12.

$$\frac{12}{36}+\frac{1}{6}+\frac{1}{9}+\frac{1}{18}$$

Reduce the fraction \frac{12}{36} to lowest terms by extracting and canceling out 12.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{1}{9} to fractions with denominator 18.

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

Since \frac{9}{18} and \frac{2}{18} have the same denominator, add them by adding their numerators.

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

Add 9 and 2 to get 11.

$$\frac{11}{18}+\frac{1}{18}$$

Since \frac{11}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{11+1}{18}$$

Add 11 and 1 to get 12.

$$\frac{12}{18}$$

Reduce the fraction \frac{12}{18} to lowest terms by extracting and canceling out 6.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$