Solve 23/4-(-11/2)+(-5/6)-(-3/8)-(+4frac{2}{3})

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

Evaluate

$$-\frac{7}{8}=-0.875$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 3 to get 11.

$$\frac{11}{4}-\left(-\frac{1\times 2+1}{2}\right)-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Multiply 1 and 2 to get 2.

$$\frac{11}{4}-\left(-\frac{2+1}{2}\right)-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Add 2 and 1 to get 3.

$$\frac{11}{4}-\left(-\frac{3}{2}\right)-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{11}{4}+\frac{3}{2}-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{11}{4}+\frac{6}{4}-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Since \frac{11}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{11+6}{4}-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Add 11 and 6 to get 17.

$$\frac{17}{4}-\frac{5}{6}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Least common multiple of 4 and 6 is 12. Convert \frac{17}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{51}{12}-\frac{10}{12}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Since \frac{51}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-10}{12}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

Subtract 10 from 51 to get 41.

$$\frac{41}{12}-\left(-\frac{3}{8}\right)-\frac{4\times 3+2}{3}$$

The opposite of -\frac{3}{8} is \frac{3}{8}.

$$\frac{41}{12}+\frac{3}{8}-\frac{4\times 3+2}{3}$$

Least common multiple of 12 and 8 is 24. Convert \frac{41}{12} and \frac{3}{8} to fractions with denominator 24.

$$\frac{82}{24}+\frac{9}{24}-\frac{4\times 3+2}{3}$$

Since \frac{82}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{82+9}{24}-\frac{4\times 3+2}{3}$$

Add 82 and 9 to get 91.

$$\frac{91}{24}-\frac{4\times 3+2}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{91}{24}-\frac{12+2}{3}$$

Add 12 and 2 to get 14.

$$\frac{91}{24}-\frac{14}{3}$$

Least common multiple of 24 and 3 is 24. Convert \frac{91}{24} and \frac{14}{3} to fractions with denominator 24.

$$\frac{91}{24}-\frac{112}{24}$$

Since \frac{91}{24} and \frac{112}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-112}{24}$$

Subtract 112 from 91 to get -21.

$$\frac{-21}{24}$$

Reduce the fraction \frac{-21}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{7}{8}$$

Factor

$$-\frac{7}{8} = -0.875$$