Solve 1/5(1/2+1/3)

$$\frac { 1 } { 5 } ( \frac { 1 } { 2 } + \frac { 1 } { 3 } )$$

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.

$$\frac{1}{5}\left(\frac{3}{6}+\frac{2}{6}\right)$$

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

$$\frac{1}{5}\times \frac{3+2}{6}$$

Add 3 and 2 to get 5.

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

Multiply \frac{1}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

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

Factor

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