Solve (3/4-7/12)-(7/12-1/4)=

$$( \frac { 3 } { 4 } - \frac { 7 } { 12 } ) - ( \frac { 7 } { 12 } - \frac { 1 } { 4 } ) =$$

Evaluate

$$-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{7}{12} to fractions with denominator 12.

$$\frac{9}{12}-\frac{7}{12}-\left(\frac{7}{12}-\frac{1}{4}\right)$$

Since \frac{9}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-7}{12}-\left(\frac{7}{12}-\frac{1}{4}\right)$$

Subtract 7 from 9 to get 2.

$$\frac{2}{12}-\left(\frac{7}{12}-\frac{1}{4}\right)$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}-\left(\frac{7}{12}-\frac{1}{4}\right)$$

Least common multiple of 12 and 4 is 12. Convert \frac{7}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{6}-\left(\frac{7}{12}-\frac{3}{12}\right)$$

Since \frac{7}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}-\frac{7-3}{12}$$

Subtract 3 from 7 to get 4.

$$\frac{1}{6}-\frac{4}{12}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

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

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

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

Since \frac{1}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 1 to get -1.

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

Factor

$$-\frac{1}{6} = -0.16666666666666666$$