Solve 12/3+(-17/8)+5/6+(-27/12)

$$1 \frac { 2 } { 3 } + ( - 1 \frac { 7 } { 8 } ) + \frac { 5 } { 6 } + ( - 2 \frac { 7 } { 12 } )$$

Evaluate

$$-\frac{47}{24}\approx -1.958333333$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{3+2}{3}-\frac{1\times 8+7}{8}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Add 3 and 2 to get 5.

$$\frac{5}{3}-\frac{1\times 8+7}{8}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Multiply 1 and 8 to get 8.

$$\frac{5}{3}-\frac{8+7}{8}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Add 8 and 7 to get 15.

$$\frac{5}{3}-\frac{15}{8}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Least common multiple of 3 and 8 is 24. Convert \frac{5}{3} and \frac{15}{8} to fractions with denominator 24.

$$\frac{40}{24}-\frac{45}{24}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Since \frac{40}{24} and \frac{45}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-45}{24}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Subtract 45 from 40 to get -5.

$$-\frac{5}{24}+\frac{5}{6}-\frac{2\times 12+7}{12}$$

Least common multiple of 24 and 6 is 24. Convert -\frac{5}{24} and \frac{5}{6} to fractions with denominator 24.

$$-\frac{5}{24}+\frac{20}{24}-\frac{2\times 12+7}{12}$$

Since -\frac{5}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$\frac{-5+20}{24}-\frac{2\times 12+7}{12}$$

Add -5 and 20 to get 15.

$$\frac{15}{24}-\frac{2\times 12+7}{12}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{5}{8}-\frac{2\times 12+7}{12}$$

Multiply 2 and 12 to get 24.

$$\frac{5}{8}-\frac{24+7}{12}$$

Add 24 and 7 to get 31.

$$\frac{5}{8}-\frac{31}{12}$$

Least common multiple of 8 and 12 is 24. Convert \frac{5}{8} and \frac{31}{12} to fractions with denominator 24.

$$\frac{15}{24}-\frac{62}{24}$$

Since \frac{15}{24} and \frac{62}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-62}{24}$$

Subtract 62 from 15 to get -47.

$$-\frac{47}{24}$$

Factor

$$-\frac{47}{24} = -1\frac{23}{24} = -1.9583333333333333$$