Solve {l}{31/30-1/10-1/15-1/20}{+frac{1}{30}}

$$\left. \begin{array} { l } { \frac { 31 } { 30 } - \frac { 1 } { 10 } - \frac { 1 } { 15 } - \frac { 1 } { 20 } } \\ { + \frac { 1 } { 30 } } \end{array} \right.$$

Evaluate

$$\frac{17}{20}=0.85$$

Solution Steps

Least common multiple of 30 and 10 is 30. Convert \frac{31}{30} and \frac{1}{10} to fractions with denominator 30.

$$\frac{31}{30}-\frac{3}{30}-\frac{1}{15}-\frac{1}{20}+\frac{1}{30}$$

Since \frac{31}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-3}{30}-\frac{1}{15}-\frac{1}{20}+\frac{1}{30}$$

Subtract 3 from 31 to get 28.

$$\frac{28}{30}-\frac{1}{15}-\frac{1}{20}+\frac{1}{30}$$

Reduce the fraction \frac{28}{30} to lowest terms by extracting and canceling out 2.

$$\frac{14}{15}-\frac{1}{15}-\frac{1}{20}+\frac{1}{30}$$

Since \frac{14}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-1}{15}-\frac{1}{20}+\frac{1}{30}$$

Subtract 1 from 14 to get 13.

$$\frac{13}{15}-\frac{1}{20}+\frac{1}{30}$$

Least common multiple of 15 and 20 is 60. Convert \frac{13}{15} and \frac{1}{20} to fractions with denominator 60.

$$\frac{52}{60}-\frac{3}{60}+\frac{1}{30}$$

Since \frac{52}{60} and \frac{3}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-3}{60}+\frac{1}{30}$$

Subtract 3 from 52 to get 49.

$$\frac{49}{60}+\frac{1}{30}$$

Least common multiple of 60 and 30 is 60. Convert \frac{49}{60} and \frac{1}{30} to fractions with denominator 60.

$$\frac{49}{60}+\frac{2}{60}$$

Since \frac{49}{60} and \frac{2}{60} have the same denominator, add them by adding their numerators.

$$\frac{49+2}{60}$$

Add 49 and 2 to get 51.

$$\frac{51}{60}$$

Reduce the fraction \frac{51}{60} to lowest terms by extracting and canceling out 3.

$$\frac{17}{20}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 5} = 0.85$$