Solve 15/3-4/9-1/6+11/18-frac{1}{36}+2

$$\frac{ 15 }{ 3 } - \frac{ 4 }{ 9 } - \frac{ 1 }{ 6 } + \frac{ 11 }{ 18 } - \frac{ 1 }{ 36 } +2$$

Evaluate

$$\frac{251}{36}\approx 6.972222222$$

Solution Steps

Divide 15 by 3 to get 5.

$$5-\frac{4}{9}-\frac{1}{6}+\frac{11}{18}-\frac{1}{36}+2$$

Convert 5 to fraction \frac{45}{9}.

$$\frac{45}{9}-\frac{4}{9}-\frac{1}{6}+\frac{11}{18}-\frac{1}{36}+2$$

Since \frac{45}{9} and \frac{4}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-4}{9}-\frac{1}{6}+\frac{11}{18}-\frac{1}{36}+2$$

Subtract 4 from 45 to get 41.

$$\frac{41}{9}-\frac{1}{6}+\frac{11}{18}-\frac{1}{36}+2$$

Least common multiple of 9 and 6 is 18. Convert \frac{41}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{82}{18}-\frac{3}{18}+\frac{11}{18}-\frac{1}{36}+2$$

Since \frac{82}{18} and \frac{3}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{82-3}{18}+\frac{11}{18}-\frac{1}{36}+2$$

Subtract 3 from 82 to get 79.

$$\frac{79}{18}+\frac{11}{18}-\frac{1}{36}+2$$

Since \frac{79}{18} and \frac{11}{18} have the same denominator, add them by adding their numerators.

$$\frac{79+11}{18}-\frac{1}{36}+2$$

Add 79 and 11 to get 90.

$$\frac{90}{18}-\frac{1}{36}+2$$

Divide 90 by 18 to get 5.

$$5-\frac{1}{36}+2$$

Convert 5 to fraction \frac{180}{36}.

$$\frac{180}{36}-\frac{1}{36}+2$$

Since \frac{180}{36} and \frac{1}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{180-1}{36}+2$$

Subtract 1 from 180 to get 179.

$$\frac{179}{36}+2$$

Convert 2 to fraction \frac{72}{36}.

$$\frac{179}{36}+\frac{72}{36}$$

Since \frac{179}{36} and \frac{72}{36} have the same denominator, add them by adding their numerators.

$$\frac{179+72}{36}$$

Add 179 and 72 to get 251.

$$\frac{251}{36}$$

Factor

$$\frac{251}{2 ^ {2} \cdot 3 ^ {2}} = 6\frac{35}{36} = 6.972222222222222$$