Solve (1/2-1/3)-(1/6-1/10)=

$$( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) - ( \frac { 1 } { 6 } - \frac { 1 } { 10 } ) =$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

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

$$\frac{3}{6}-\frac{2}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)$$

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

$$\frac{3-2}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)$$

Subtract 2 from 3 to get 1.

$$\frac{1}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)$$

Least common multiple of 6 and 10 is 30. Convert \frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{1}{6}-\left(\frac{5}{30}-\frac{3}{30}\right)$$

Since \frac{5}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}-\frac{5-3}{30}$$

Subtract 3 from 5 to get 2.

$$\frac{1}{6}-\frac{2}{30}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}-\frac{1}{15}$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{1}{15} to fractions with denominator 30.

$$\frac{5}{30}-\frac{2}{30}$$

Since \frac{5}{30} and \frac{2}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{30}$$

Subtract 2 from 5 to get 3.

$$\frac{3}{30}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$