Solve 1/2(1/5-1/10)+1/3(frac{1}{2}-frac{1}{4})=

$$\frac { 1 } { 2 } ( \frac { 1 } { 5 } - \frac { 1 } { 10 } ) + \frac { 1 } { 3 } ( \frac { 1 } { 2 } - \frac { 1 } { 4 } ) =$$

Evaluate

$$\frac{2}{15}\approx 0.133333333$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{1}{2}\left(\frac{2}{10}-\frac{1}{10}\right)+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)$$

Since \frac{2}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{2-1}{10}+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)$$

Subtract 1 from 2 to get 1.

$$\frac{1}{2}\times \frac{1}{10}+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)$$

Multiply \frac{1}{2} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{2\times 10}+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 10}.

$$\frac{1}{20}+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{1}{20}+\frac{1}{3}\left(\frac{2}{4}-\frac{1}{4}\right)$$

Since \frac{2}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{20}+\frac{1}{3}\times \frac{2-1}{4}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{20}+\frac{1}{3}\times \frac{1}{4}$$

Multiply \frac{1}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{20}+\frac{1\times 1}{3\times 4}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 4}.

$$\frac{1}{20}+\frac{1}{12}$$

Least common multiple of 20 and 12 is 60. Convert \frac{1}{20} and \frac{1}{12} to fractions with denominator 60.

$$\frac{3}{60}+\frac{5}{60}$$

Since \frac{3}{60} and \frac{5}{60} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{60}$$

Add 3 and 5 to get 8.

$$\frac{8}{60}$$

Reduce the fraction \frac{8}{60} to lowest terms by extracting and canceling out 4.

$$\frac{2}{15}$$

Factor

$$\frac{2}{3 \cdot 5} = 0.13333333333333333$$