Solve (5/6-5/10)-(2/3-3/4)=

$$( \frac { 5 } { 6 } - \frac { 5 } { 10 } ) - ( \frac { 2 } { 3 } - \frac { 3 } { 4 } ) =$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{5}{6}-\frac{1}{2}-\left(\frac{2}{3}-\frac{3}{4}\right)$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{6}-\frac{3}{6}-\left(\frac{2}{3}-\frac{3}{4}\right)$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-3}{6}-\left(\frac{2}{3}-\frac{3}{4}\right)$$

Subtract 3 from 5 to get 2.

$$\frac{2}{6}-\left(\frac{2}{3}-\frac{3}{4}\right)$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{1}{3}-\left(\frac{8}{12}-\frac{9}{12}\right)$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}-\frac{8-9}{12}$$

Subtract 9 from 8 to get -1.

$$\frac{1}{3}-\left(-\frac{1}{12}\right)$$

The opposite of -\frac{1}{12} is \frac{1}{12}.

$$\frac{1}{3}+\frac{1}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{1}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{4}{12}+\frac{1}{12}$$

Since \frac{4}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{4+1}{12}$$

Add 4 and 1 to get 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$