Solve 5/12(36/15){(5/4-9/4)-[frac{3}{4}-(-frac{5}{6})-frac{7}{4}]}

$$\frac { 5 } { 12 } ( \frac { 36 } { 15 } ) \{ ( \frac { 5 } { 4 } - \frac { 9 } { 4 } ) - [ \frac { 3 } { 4 } - ( - \frac { 5 } { 6 } ) - \frac { 7 } { 4 } ] \}$$

Evaluate

$$-\frac{5}{6}\approx -0.833333333$$

Solution Steps

Reduce the fraction \frac{36}{15} to lowest terms by extracting and canceling out 3.

$$\frac{5}{12}\times \frac{12}{5}\left(\frac{5}{4}-\frac{9}{4}-\left(\frac{3}{4}-\left(-\frac{5}{6}\right)-\frac{7}{4}\right)\right)$$

Cancel out \frac{5}{12} and its reciprocal \frac{12}{5}.

$$\frac{5}{4}-\frac{9}{4}-\left(\frac{3}{4}-\left(-\frac{5}{6}\right)-\frac{7}{4}\right)$$

Since \frac{5}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-9}{4}-\left(\frac{3}{4}-\left(-\frac{5}{6}\right)-\frac{7}{4}\right)$$

Subtract 9 from 5 to get -4.

$$\frac{-4}{4}-\left(\frac{3}{4}-\left(-\frac{5}{6}\right)-\frac{7}{4}\right)$$

Divide -4 by 4 to get -1.

$$-1-\left(\frac{3}{4}-\left(-\frac{5}{6}\right)-\frac{7}{4}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$-1-\left(\frac{3}{4}+\frac{5}{6}-\frac{7}{4}\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{5}{6} to fractions with denominator 12.

$$-1-\left(\frac{9}{12}+\frac{10}{12}-\frac{7}{4}\right)$$

Since \frac{9}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$-1-\left(\frac{9+10}{12}-\frac{7}{4}\right)$$

Add 9 and 10 to get 19.

$$-1-\left(\frac{19}{12}-\frac{7}{4}\right)$$

Least common multiple of 12 and 4 is 12. Convert \frac{19}{12} and \frac{7}{4} to fractions with denominator 12.

$$-1-\left(\frac{19}{12}-\frac{21}{12}\right)$$

Since \frac{19}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$-1-\frac{19-21}{12}$$

Subtract 21 from 19 to get -2.

$$-1-\frac{-2}{12}$$

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

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

The opposite of -\frac{1}{6} is \frac{1}{6}.

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

Convert -1 to fraction -\frac{6}{6}.

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

Since -\frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

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

Add -6 and 1 to get -5.

$$-\frac{5}{6}$$

Factor

$$-\frac{5}{6} = -0.8333333333333334$$