Solve 3/2-2/5+8/12-3/9+frac{15}{6}=

$$\frac { 3 } { 2 } - \frac { 2 } { 5 } + \frac { 8 } { 12 } - \frac { 3 } { 9 } + \frac { 15 } { 6 } =$$

Evaluate

$$\frac{59}{15}\approx 3.933333333$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{15}{10}-\frac{4}{10}+\frac{8}{12}-\frac{3}{9}+\frac{15}{6}$$

Since \frac{15}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-4}{10}+\frac{8}{12}-\frac{3}{9}+\frac{15}{6}$$

Subtract 4 from 15 to get 11.

$$\frac{11}{10}+\frac{8}{12}-\frac{3}{9}+\frac{15}{6}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\frac{11}{10}+\frac{2}{3}-\frac{3}{9}+\frac{15}{6}$$

Least common multiple of 10 and 3 is 30. Convert \frac{11}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{33}{30}+\frac{20}{30}-\frac{3}{9}+\frac{15}{6}$$

Since \frac{33}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{33+20}{30}-\frac{3}{9}+\frac{15}{6}$$

Add 33 and 20 to get 53.

$$\frac{53}{30}-\frac{3}{9}+\frac{15}{6}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{53}{30}-\frac{1}{3}+\frac{15}{6}$$

Least common multiple of 30 and 3 is 30. Convert \frac{53}{30} and \frac{1}{3} to fractions with denominator 30.

$$\frac{53}{30}-\frac{10}{30}+\frac{15}{6}$$

Since \frac{53}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{53-10}{30}+\frac{15}{6}$$

Subtract 10 from 53 to get 43.

$$\frac{43}{30}+\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{43}{30}+\frac{5}{2}$$

Least common multiple of 30 and 2 is 30. Convert \frac{43}{30} and \frac{5}{2} to fractions with denominator 30.

$$\frac{43}{30}+\frac{75}{30}$$

Since \frac{43}{30} and \frac{75}{30} have the same denominator, add them by adding their numerators.

$$\frac{43+75}{30}$$

Add 43 and 75 to get 118.

$$\frac{118}{30}$$

Reduce the fraction \frac{118}{30} to lowest terms by extracting and canceling out 2.

$$\frac{59}{15}$$

Factor

$$\frac{59}{3 \cdot 5} = 3\frac{14}{15} = 3.933333333333333$$