Solve 62/3-(-33/4)+(-25/6)-(53/8)-3frac{1}{3}

$$6 \frac { 2 } { 3 } - ( - 3 \frac { 3 } { 4 } ) + ( - 2 \frac { 5 } { 6 } ) - ( 5 \frac { 3 } { 8 } ) - 3 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{9}{8}=-1.125$$

Solution Steps

Multiply 6 and 3 to get 18.

$$\frac{18+2}{3}-\left(-\frac{3\times 4+3}{4}\right)-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Add 18 and 2 to get 20.

$$\frac{20}{3}-\left(-\frac{3\times 4+3}{4}\right)-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Multiply 3 and 4 to get 12.

$$\frac{20}{3}-\left(-\frac{12+3}{4}\right)-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Add 12 and 3 to get 15.

$$\frac{20}{3}-\left(-\frac{15}{4}\right)-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

The opposite of -\frac{15}{4} is \frac{15}{4}.

$$\frac{20}{3}+\frac{15}{4}-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Least common multiple of 3 and 4 is 12. Convert \frac{20}{3} and \frac{15}{4} to fractions with denominator 12.

$$\frac{80}{12}+\frac{45}{12}-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Since \frac{80}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.

$$\frac{80+45}{12}-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Add 80 and 45 to get 125.

$$\frac{125}{12}-\frac{2\times 6+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Multiply 2 and 6 to get 12.

$$\frac{125}{12}-\frac{12+5}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Add 12 and 5 to get 17.

$$\frac{125}{12}-\frac{17}{6}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Least common multiple of 12 and 6 is 12. Convert \frac{125}{12} and \frac{17}{6} to fractions with denominator 12.

$$\frac{125}{12}-\frac{34}{12}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Since \frac{125}{12} and \frac{34}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{125-34}{12}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Subtract 34 from 125 to get 91.

$$\frac{91}{12}-\frac{5\times 8+3}{8}-\frac{3\times 3+1}{3}$$

Multiply 5 and 8 to get 40.

$$\frac{91}{12}-\frac{40+3}{8}-\frac{3\times 3+1}{3}$$

Add 40 and 3 to get 43.

$$\frac{91}{12}-\frac{43}{8}-\frac{3\times 3+1}{3}$$

Least common multiple of 12 and 8 is 24. Convert \frac{91}{12} and \frac{43}{8} to fractions with denominator 24.

$$\frac{182}{24}-\frac{129}{24}-\frac{3\times 3+1}{3}$$

Since \frac{182}{24} and \frac{129}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{182-129}{24}-\frac{3\times 3+1}{3}$$

Subtract 129 from 182 to get 53.

$$\frac{53}{24}-\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{53}{24}-\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$\frac{53}{24}-\frac{10}{3}$$

Least common multiple of 24 and 3 is 24. Convert \frac{53}{24} and \frac{10}{3} to fractions with denominator 24.

$$\frac{53}{24}-\frac{80}{24}$$

Since \frac{53}{24} and \frac{80}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53-80}{24}$$

Subtract 80 from 53 to get -27.

$$\frac{-27}{24}$$

Reduce the fraction \frac{-27}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{8}$$

Factor

$$-\frac{9}{8} = -1\frac{1}{8} = -1.125$$