Solve 3/2+7/6+13/12+21/20+frac{31}{30}

$$\frac { 3 } { 2 } + \frac { 7 } { 6 } + \frac { 13 } { 12 } + \frac { 21 } { 20 } + \frac { 31 } { 30 }$$

Evaluate

$$\frac{35}{6}\approx 5.833333333$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{7}{6} to fractions with denominator 6.

$$\frac{9}{6}+\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}$$

Since \frac{9}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}$$

Add 9 and 7 to get 16.

$$\frac{16}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}$$

Least common multiple of 3 and 12 is 12. Convert \frac{8}{3} and \frac{13}{12} to fractions with denominator 12.

$$\frac{32}{12}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}$$

Since \frac{32}{12} and \frac{13}{12} have the same denominator, add them by adding their numerators.

$$\frac{32+13}{12}+\frac{21}{20}+\frac{31}{30}$$

Add 32 and 13 to get 45.

$$\frac{45}{12}+\frac{21}{20}+\frac{31}{30}$$

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$\frac{15}{4}+\frac{21}{20}+\frac{31}{30}$$

Least common multiple of 4 and 20 is 20. Convert \frac{15}{4} and \frac{21}{20} to fractions with denominator 20.

$$\frac{75}{20}+\frac{21}{20}+\frac{31}{30}$$

Since \frac{75}{20} and \frac{21}{20} have the same denominator, add them by adding their numerators.

$$\frac{75+21}{20}+\frac{31}{30}$$

Add 75 and 21 to get 96.

$$\frac{96}{20}+\frac{31}{30}$$

Reduce the fraction \frac{96}{20} to lowest terms by extracting and canceling out 4.

$$\frac{24}{5}+\frac{31}{30}$$

Least common multiple of 5 and 30 is 30. Convert \frac{24}{5} and \frac{31}{30} to fractions with denominator 30.

$$\frac{144}{30}+\frac{31}{30}$$

Since \frac{144}{30} and \frac{31}{30} have the same denominator, add them by adding their numerators.

$$\frac{144+31}{30}$$

Add 144 and 31 to get 175.

$$\frac{175}{30}$$

Reduce the fraction \frac{175}{30} to lowest terms by extracting and canceling out 5.

$$\frac{35}{6}$$

Factor

$$\frac{5 \cdot 7}{2 \cdot 3} = 5\frac{5}{6} = 5.833333333333333$$