Solve 9/4+1/3-3/2-1/20+frac{27}{4}+9

$$\frac { 9 } { 4 } + \frac { 1 } { 3 } - \frac { 3 } { 2 } - \frac { 1 } { 20 } + \frac { 27 } { 4 } + 9$$

Evaluate

$$\frac{1007}{60}\approx 16.783333333$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{9}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{27}{12}+\frac{4}{12}-\frac{3}{2}-\frac{1}{20}+\frac{27}{4}+9$$

Since \frac{27}{12} and \frac{4}{12} have the same denominator, add them by adding their numerators.

$$\frac{27+4}{12}-\frac{3}{2}-\frac{1}{20}+\frac{27}{4}+9$$

Add 27 and 4 to get 31.

$$\frac{31}{12}-\frac{3}{2}-\frac{1}{20}+\frac{27}{4}+9$$

Least common multiple of 12 and 2 is 12. Convert \frac{31}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{31}{12}-\frac{18}{12}-\frac{1}{20}+\frac{27}{4}+9$$

Since \frac{31}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-18}{12}-\frac{1}{20}+\frac{27}{4}+9$$

Subtract 18 from 31 to get 13.

$$\frac{13}{12}-\frac{1}{20}+\frac{27}{4}+9$$

Least common multiple of 12 and 20 is 60. Convert \frac{13}{12} and \frac{1}{20} to fractions with denominator 60.

$$\frac{65}{60}-\frac{3}{60}+\frac{27}{4}+9$$

Since \frac{65}{60} and \frac{3}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-3}{60}+\frac{27}{4}+9$$

Subtract 3 from 65 to get 62.

$$\frac{62}{60}+\frac{27}{4}+9$$

Reduce the fraction \frac{62}{60} to lowest terms by extracting and canceling out 2.

$$\frac{31}{30}+\frac{27}{4}+9$$

Least common multiple of 30 and 4 is 60. Convert \frac{31}{30} and \frac{27}{4} to fractions with denominator 60.

$$\frac{62}{60}+\frac{405}{60}+9$$

Since \frac{62}{60} and \frac{405}{60} have the same denominator, add them by adding their numerators.

$$\frac{62+405}{60}+9$$

Add 62 and 405 to get 467.

$$\frac{467}{60}+9$$

Convert 9 to fraction \frac{540}{60}.

$$\frac{467}{60}+\frac{540}{60}$$

Since \frac{467}{60} and \frac{540}{60} have the same denominator, add them by adding their numerators.

$$\frac{467+540}{60}$$

Add 467 and 540 to get 1007.

$$\frac{1007}{60}$$

Factor

$$\frac{19 \cdot 53}{2 ^ {2} \cdot 3 \cdot 5} = 16\frac{47}{60} = 16.783333333333335$$