Solve 2.1+(-7/8)+11/6-7.5

$$2.1 + ( - \frac { 7 } { 8 } ) + \frac { 11 } { 6 } - 7.5$$

Evaluate

$$-\frac{533}{120}\approx -4.441666667$$

Solution Steps

Convert decimal number 2.1 to fraction \frac{21}{10}.

$$\frac{21}{10}-\frac{7}{8}+\frac{11}{6}-7.5$$

Least common multiple of 10 and 8 is 40. Convert \frac{21}{10} and \frac{7}{8} to fractions with denominator 40.

$$\frac{84}{40}-\frac{35}{40}+\frac{11}{6}-7.5$$

Since \frac{84}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{84-35}{40}+\frac{11}{6}-7.5$$

Subtract 35 from 84 to get 49.

$$\frac{49}{40}+\frac{11}{6}-7.5$$

Least common multiple of 40 and 6 is 120. Convert \frac{49}{40} and \frac{11}{6} to fractions with denominator 120.

$$\frac{147}{120}+\frac{220}{120}-7.5$$

Since \frac{147}{120} and \frac{220}{120} have the same denominator, add them by adding their numerators.

$$\frac{147+220}{120}-7.5$$

Add 147 and 220 to get 367.

$$\frac{367}{120}-7.5$$

Convert decimal number 7.5 to fraction \frac{75}{10}. Reduce the fraction \frac{75}{10} to lowest terms by extracting and canceling out 5.

$$\frac{367}{120}-\frac{15}{2}$$

Least common multiple of 120 and 2 is 120. Convert \frac{367}{120} and \frac{15}{2} to fractions with denominator 120.

$$\frac{367}{120}-\frac{900}{120}$$

Since \frac{367}{120} and \frac{900}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{367-900}{120}$$

Subtract 900 from 367 to get -533.

$$-\frac{533}{120}$$

Factor

$$-\frac{533}{120} = -4\frac{53}{120} = -4.441666666666666$$