Solve (1/3-1/5)1/2+1/6divfrac{1}{3}

$$( \frac { 1 } { 3 } - \frac { 1 } { 5 } ) \frac { 1 } { 2 } + \frac { 1 } { 6 } \div \frac { 1 } { 3 }$$

Evaluate

$$\frac{17}{30}\approx 0.566666667$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{1}{5} to fractions with denominator 15.

$$\left(\frac{5}{15}-\frac{3}{15}\right)\times \frac{1}{2}+\frac{\frac{1}{6}}{\frac{1}{3}}$$

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-3}{15}\times \frac{1}{2}+\frac{\frac{1}{6}}{\frac{1}{3}}$$

Subtract 3 from 5 to get 2.

$$\frac{2}{15}\times \frac{1}{2}+\frac{\frac{1}{6}}{\frac{1}{3}}$$

Multiply \frac{2}{15} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{15\times 2}+\frac{\frac{1}{6}}{\frac{1}{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{15}+\frac{\frac{1}{6}}{\frac{1}{3}}$$

Divide \frac{1}{6} by \frac{1}{3} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{3}.

$$\frac{1}{15}+\frac{1}{6}\times 3$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{15}+\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{15}+\frac{1}{2}$$

Least common multiple of 15 and 2 is 30. Convert \frac{1}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{2}{30}+\frac{15}{30}$$

Since \frac{2}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{2+15}{30}$$

Add 2 and 15 to get 17.

$$\frac{17}{30}$$

Factor

$$\frac{17}{2 \cdot 3 \cdot 5} = 0.5666666666666667$$