Solve -51/8-(2/3-21/8)+11/3

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

Evaluate

$$-\frac{7}{3}\approx -2.333333333$$

Solution Steps

Multiply 5 and 8 to get 40.

$$-\frac{40+1}{8}-\left(\frac{2}{3}-\frac{2\times 8+1}{8}\right)+\frac{1\times 3+1}{3}$$

Add 40 and 1 to get 41.

$$-\frac{41}{8}-\left(\frac{2}{3}-\frac{2\times 8+1}{8}\right)+\frac{1\times 3+1}{3}$$

Multiply 2 and 8 to get 16.

$$-\frac{41}{8}-\left(\frac{2}{3}-\frac{16+1}{8}\right)+\frac{1\times 3+1}{3}$$

Add 16 and 1 to get 17.

$$-\frac{41}{8}-\left(\frac{2}{3}-\frac{17}{8}\right)+\frac{1\times 3+1}{3}$$

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{17}{8} to fractions with denominator 24.

$$-\frac{41}{8}-\left(\frac{16}{24}-\frac{51}{24}\right)+\frac{1\times 3+1}{3}$$

Since \frac{16}{24} and \frac{51}{24} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{41}{8}-\frac{16-51}{24}+\frac{1\times 3+1}{3}$$

Subtract 51 from 16 to get -35.

$$-\frac{41}{8}-\left(-\frac{35}{24}\right)+\frac{1\times 3+1}{3}$$

The opposite of -\frac{35}{24} is \frac{35}{24}.

$$-\frac{41}{8}+\frac{35}{24}+\frac{1\times 3+1}{3}$$

Least common multiple of 8 and 24 is 24. Convert -\frac{41}{8} and \frac{35}{24} to fractions with denominator 24.

$$-\frac{123}{24}+\frac{35}{24}+\frac{1\times 3+1}{3}$$

Since -\frac{123}{24} and \frac{35}{24} have the same denominator, add them by adding their numerators.

$$\frac{-123+35}{24}+\frac{1\times 3+1}{3}$$

Add -123 and 35 to get -88.

$$\frac{-88}{24}+\frac{1\times 3+1}{3}$$

Reduce the fraction \frac{-88}{24} to lowest terms by extracting and canceling out 8.

$$-\frac{11}{3}+\frac{1\times 3+1}{3}$$

Multiply 1 and 3 to get 3.

$$-\frac{11}{3}+\frac{3+1}{3}$$

Add 3 and 1 to get 4.

$$-\frac{11}{3}+\frac{4}{3}$$

Since -\frac{11}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{-11+4}{3}$$

Add -11 and 4 to get -7.

$$-\frac{7}{3}$$

Factor

$$-\frac{7}{3} = -2\frac{1}{3} = -2.3333333333333335$$