Solve 112/9-(-1/18)+1/2

$$11 \frac { 2 } { 9 } - ( - \frac { 1 } { 18 } ) + \frac { 1 } { 2 }$$

Evaluate

$$\frac{106}{9}\approx 11.777777778$$

Solution Steps

Multiply 11 and 9 to get 99.

$$\frac{99+2}{9}-\left(-\frac{1}{18}\right)+\frac{1}{2}$$

Add 99 and 2 to get 101.

$$\frac{101}{9}-\left(-\frac{1}{18}\right)+\frac{1}{2}$$

The opposite of -\frac{1}{18} is \frac{1}{18}.

$$\frac{101}{9}+\frac{1}{18}+\frac{1}{2}$$

Least common multiple of 9 and 18 is 18. Convert \frac{101}{9} and \frac{1}{18} to fractions with denominator 18.

$$\frac{202}{18}+\frac{1}{18}+\frac{1}{2}$$

Since \frac{202}{18} and \frac{1}{18} have the same denominator, add them by adding their numerators.

$$\frac{202+1}{18}+\frac{1}{2}$$

Add 202 and 1 to get 203.

$$\frac{203}{18}+\frac{1}{2}$$

Least common multiple of 18 and 2 is 18. Convert \frac{203}{18} and \frac{1}{2} to fractions with denominator 18.

$$\frac{203}{18}+\frac{9}{18}$$

Since \frac{203}{18} and \frac{9}{18} have the same denominator, add them by adding their numerators.

$$\frac{203+9}{18}$$

Add 203 and 9 to get 212.

$$\frac{212}{18}$$

Reduce the fraction \frac{212}{18} to lowest terms by extracting and canceling out 2.

$$\frac{106}{9}$$

Factor

$$\frac{2 \cdot 53}{3 ^ {2}} = 11\frac{7}{9} = 11.777777777777779$$