Solve 7/24-[(5/12-1/8)-(-7/6+frac{3}{4})]

$$\frac { 7 } { 24 } - [ ( \frac { 5 } { 12 } - \frac { 1 } { 8 } ) - ( - \frac { 7 } { 6 } + \frac { 3 } { 4 } ) ]$$

Evaluate

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

Solution Steps

Least common multiple of 12 and 8 is 24. Convert \frac{5}{12} and \frac{1}{8} to fractions with denominator 24.

$$\frac{7}{24}-\left(\frac{10}{24}-\frac{3}{24}-\left(-\frac{7}{6}+\frac{3}{4}\right)\right)$$

Since \frac{10}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{24}-\left(\frac{10-3}{24}-\left(-\frac{7}{6}+\frac{3}{4}\right)\right)$$

Subtract 3 from 10 to get 7.

$$\frac{7}{24}-\left(\frac{7}{24}-\left(-\frac{7}{6}+\frac{3}{4}\right)\right)$$

Least common multiple of 6 and 4 is 12. Convert -\frac{7}{6} and \frac{3}{4} to fractions with denominator 12.

$$\frac{7}{24}-\left(\frac{7}{24}-\left(-\frac{14}{12}+\frac{9}{12}\right)\right)$$

Since -\frac{14}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{7}{24}-\left(\frac{7}{24}-\frac{-14+9}{12}\right)$$

Add -14 and 9 to get -5.

$$\frac{7}{24}-\left(\frac{7}{24}-\left(-\frac{5}{12}\right)\right)$$

The opposite of -\frac{5}{12} is \frac{5}{12}.

$$\frac{7}{24}-\left(\frac{7}{24}+\frac{5}{12}\right)$$

Least common multiple of 24 and 12 is 24. Convert \frac{7}{24} and \frac{5}{12} to fractions with denominator 24.

$$\frac{7}{24}-\left(\frac{7}{24}+\frac{10}{24}\right)$$

Since \frac{7}{24} and \frac{10}{24} have the same denominator, add them by adding their numerators.

$$\frac{7}{24}-\frac{7+10}{24}$$

Add 7 and 10 to get 17.

$$\frac{7}{24}-\frac{17}{24}$$

Since \frac{7}{24} and \frac{17}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-17}{24}$$

Subtract 17 from 7 to get -10.

$$\frac{-10}{24}$$

Reduce the fraction \frac{-10}{24} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{5}{12} = -0.4166666666666667$$