Solve (7/4-5/12+5/6-1/3)*(-36)

$$( \frac { 7 } { 4 } - \frac { 5 } { 12 } + \frac { 5 } { 6 } - \frac { 1 } { 3 } ) \times ( - 36 )$$

Evaluate

$$-66$$

Solution Steps

Least common multiple of 4 and 12 is 12. Convert \frac{7}{4} and \frac{5}{12} to fractions with denominator 12.

$$\left(\frac{21}{12}-\frac{5}{12}+\frac{5}{6}-\frac{1}{3}\right)\left(-36\right)$$

Since \frac{21}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{21-5}{12}+\frac{5}{6}-\frac{1}{3}\right)\left(-36\right)$$

Subtract 5 from 21 to get 16.

$$\left(\frac{16}{12}+\frac{5}{6}-\frac{1}{3}\right)\left(-36\right)$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

$$\left(\frac{4}{3}+\frac{5}{6}-\frac{1}{3}\right)\left(-36\right)$$

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

$$\left(\frac{8}{6}+\frac{5}{6}-\frac{1}{3}\right)\left(-36\right)$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\left(\frac{8+5}{6}-\frac{1}{3}\right)\left(-36\right)$$

Add 8 and 5 to get 13.

$$\left(\frac{13}{6}-\frac{1}{3}\right)\left(-36\right)$$

Least common multiple of 6 and 3 is 6. Convert \frac{13}{6} and \frac{1}{3} to fractions with denominator 6.

$$\left(\frac{13}{6}-\frac{2}{6}\right)\left(-36\right)$$

Since \frac{13}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-2}{6}\left(-36\right)$$

Subtract 2 from 13 to get 11.

$$\frac{11}{6}\left(-36\right)$$

Express \frac{11}{6}\left(-36\right) as a single fraction.

$$\frac{11\left(-36\right)}{6}$$

Multiply 11 and -36 to get -396.

$$\frac{-396}{6}$$

Divide -396 by 6 to get -66.

$$-66$$

Factor

$$-66$$