Solve 3+(-13/6)+(-3)+(+7/2)+(-5/2)+(+23/6)+(+frac{1}{2})

$$3 + ( - \frac { 13 } { 6 } ) + ( - 3 ) + ( + \frac { 7 } { 2 } ) + ( - \frac { 5 } { 2 } ) + ( + \frac { 23 } { 6 } ) + ( + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{19}{6}\approx 3.166666667$$

Solution Steps

Convert 3 to fraction \frac{18}{6}.

$$\frac{18}{6}-\frac{13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Since \frac{18}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-13}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Subtract 13 from 18 to get 5.

$$\frac{5}{6}-3+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{5}{6}-\frac{18}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Since \frac{5}{6} and \frac{18}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-18}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Subtract 18 from 5 to get -13.

$$-\frac{13}{6}+\frac{7}{2}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{13}{6} and \frac{7}{2} to fractions with denominator 6.

$$-\frac{13}{6}+\frac{21}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Since -\frac{13}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{-13+21}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Add -13 and 21 to get 8.

$$\frac{8}{6}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}-\frac{5}{2}+\frac{23}{6}+\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{8}{6}-\frac{15}{6}+\frac{23}{6}+\frac{1}{2}$$

Since \frac{8}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-15}{6}+\frac{23}{6}+\frac{1}{2}$$

Subtract 15 from 8 to get -7.

$$-\frac{7}{6}+\frac{23}{6}+\frac{1}{2}$$

Since -\frac{7}{6} and \frac{23}{6} have the same denominator, add them by adding their numerators.

$$\frac{-7+23}{6}+\frac{1}{2}$$

Add -7 and 23 to get 16.

$$\frac{16}{6}+\frac{1}{2}$$

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

$$\frac{8}{3}+\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{16}{6}+\frac{3}{6}$$

Since \frac{16}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{16+3}{6}$$

Add 16 and 3 to get 19.

$$\frac{19}{6}$$

Factor

$$\frac{19}{2 \cdot 3} = 3\frac{1}{6} = 3.1666666666666665$$