Solve 1/2+1/18+1/18+1/18+frac{1}{18}+frac{1}{18}

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

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

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

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

Since \frac{9}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

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

Add 9 and 1 to get 10.

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

Since \frac{10}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

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

Add 10 and 1 to get 11.

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

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

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

Add 11 and 1 to get 12.

$$\frac{12}{18}+\frac{1}{18}+\frac{1}{18}$$

Since \frac{12}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{12+1}{18}+\frac{1}{18}$$

Add 12 and 1 to get 13.

$$\frac{13}{18}+\frac{1}{18}$$

Since \frac{13}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{13+1}{18}$$

Add 13 and 1 to get 14.

$$\frac{14}{18}$$

Reduce the fraction \frac{14}{18} to lowest terms by extracting and canceling out 2.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$