Solve 1-|1/2+1/3|

$$1 - | \frac { 1 } { 2 } + \frac { 1 } { 3 } |$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

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

$$1-|\frac{3}{6}+\frac{2}{6}|$$

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

$$1-|\frac{3+2}{6}|$$

Add 3 and 2 to get 5.

$$1-|\frac{5}{6}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{5}{6} is \frac{5}{6}.

$$1-\frac{5}{6}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{6}{6}-\frac{5}{6}$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{6}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$