Solve (-55/6+63/8-17/15)*120

$$( - 5 \frac { 5 } { 6 } + 6 \frac { 3 } { 8 } - 1 \frac { 7 } { 15 } ) \times 120$$

Evaluate

$$-111$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\left(-\frac{30+5}{6}+\frac{6\times 8+3}{8}-\frac{1\times 15+7}{15}\right)\times 120$$

Add 30 and 5 to get 35.

$$\left(-\frac{35}{6}+\frac{6\times 8+3}{8}-\frac{1\times 15+7}{15}\right)\times 120$$

Multiply 6 and 8 to get 48.

$$\left(-\frac{35}{6}+\frac{48+3}{8}-\frac{1\times 15+7}{15}\right)\times 120$$

Add 48 and 3 to get 51.

$$\left(-\frac{35}{6}+\frac{51}{8}-\frac{1\times 15+7}{15}\right)\times 120$$

Least common multiple of 6 and 8 is 24. Convert -\frac{35}{6} and \frac{51}{8} to fractions with denominator 24.

$$\left(-\frac{140}{24}+\frac{153}{24}-\frac{1\times 15+7}{15}\right)\times 120$$

Since -\frac{140}{24} and \frac{153}{24} have the same denominator, add them by adding their numerators.

$$\left(\frac{-140+153}{24}-\frac{1\times 15+7}{15}\right)\times 120$$

Add -140 and 153 to get 13.

$$\left(\frac{13}{24}-\frac{1\times 15+7}{15}\right)\times 120$$

Multiply 1 and 15 to get 15.

$$\left(\frac{13}{24}-\frac{15+7}{15}\right)\times 120$$

Add 15 and 7 to get 22.

$$\left(\frac{13}{24}-\frac{22}{15}\right)\times 120$$

Least common multiple of 24 and 15 is 120. Convert \frac{13}{24} and \frac{22}{15} to fractions with denominator 120.

$$\left(\frac{65}{120}-\frac{176}{120}\right)\times 120$$

Since \frac{65}{120} and \frac{176}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-176}{120}\times 120$$

Subtract 176 from 65 to get -111.

$$\frac{-111}{120}\times 120$$

Reduce the fraction \frac{-111}{120} to lowest terms by extracting and canceling out 3.

$$-\frac{37}{40}\times 120$$

Express -\frac{37}{40}\times 120 as a single fraction.

$$\frac{-37\times 120}{40}$$

Multiply -37 and 120 to get -4440.

$$\frac{-4440}{40}$$

Divide -4440 by 40 to get -111.

$$-111$$

Factor

$$-111$$