Solve 1/2+3/2-6/5+8/4-frac{9}{2}+frac{13}{6}=

$$\frac { 1 } { 2 } + \frac { 3 } { 2 } - \frac { 6 } { 5 } + \frac { 8 } { 4 } - \frac { 9 } { 2 } + \frac { 13 } { 6 } =$$

Evaluate

$$\frac{7}{15}\approx 0.466666667$$

Solution Steps

Since \frac{1}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{2}-\frac{6}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Add 1 and 3 to get 4.

$$\frac{4}{2}-\frac{6}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Divide 4 by 2 to get 2.

$$2-\frac{6}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{10}{5}-\frac{6}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Since \frac{10}{5} and \frac{6}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-6}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Subtract 6 from 10 to get 4.

$$\frac{4}{5}+\frac{8}{4}-\frac{9}{2}+\frac{13}{6}$$

Divide 8 by 4 to get 2.

$$\frac{4}{5}+2-\frac{9}{2}+\frac{13}{6}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{4}{5}+\frac{10}{5}-\frac{9}{2}+\frac{13}{6}$$

Since \frac{4}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{4+10}{5}-\frac{9}{2}+\frac{13}{6}$$

Add 4 and 10 to get 14.

$$\frac{14}{5}-\frac{9}{2}+\frac{13}{6}$$

Least common multiple of 5 and 2 is 10. Convert \frac{14}{5} and \frac{9}{2} to fractions with denominator 10.

$$\frac{28}{10}-\frac{45}{10}+\frac{13}{6}$$

Since \frac{28}{10} and \frac{45}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-45}{10}+\frac{13}{6}$$

Subtract 45 from 28 to get -17.

$$-\frac{17}{10}+\frac{13}{6}$$

Least common multiple of 10 and 6 is 30. Convert -\frac{17}{10} and \frac{13}{6} to fractions with denominator 30.

$$-\frac{51}{30}+\frac{65}{30}$$

Since -\frac{51}{30} and \frac{65}{30} have the same denominator, add them by adding their numerators.

$$\frac{-51+65}{30}$$

Add -51 and 65 to get 14.

$$\frac{14}{30}$$

Reduce the fraction \frac{14}{30} to lowest terms by extracting and canceling out 2.

$$\frac{7}{15}$$

Factor

$$\frac{7}{3 \cdot 5} = 0.4666666666666667$$