Solve 12-3r/2+21/2+31/2-k/3

$$12 - \frac { 3 r } { 2 } + \frac { 21 } { 2 } + \frac { 31 } { 2 } - \frac { k } { 3 }$$

Evaluate

$$-\frac{k}{3}-\frac{3r}{2}+38$$

Short Solution Steps

Convert 12 to fraction \frac{24}{2}.

$$\frac{24}{2}-\frac{3r}{2}+\frac{21}{2}+\frac{31}{2}-\frac{k}{3}$$

Since \frac{24}{2} and \frac{21}{2} have the same denominator, add them by adding their numerators.

$$\frac{24+21}{2}-\frac{3r}{2}+\frac{31}{2}-\frac{k}{3}$$

Add 24 and 21 to get 45.

$$\frac{45}{2}-\frac{3r}{2}+\frac{31}{2}-\frac{k}{3}$$

Since \frac{45}{2} and \frac{31}{2} have the same denominator, add them by adding their numerators.

$$\frac{45+31}{2}-\frac{3r}{2}-\frac{k}{3}$$

Add 45 and 31 to get 76.

$$\frac{76}{2}-\frac{3r}{2}-\frac{k}{3}$$

Divide 76 by 2 to get 38.

$$38-\frac{3r}{2}-\frac{k}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 38 times \frac{2}{2}.

$$\frac{38\times 2}{2}-\frac{3r}{2}-\frac{k}{3}$$

Since \frac{38\times 2}{2} and \frac{3r}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38\times 2-3r}{2}-\frac{k}{3}$$

Do the multiplications in 38\times 2-3r.

$$\frac{76-3r}{2}-\frac{k}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{76-3r}{2} times \frac{3}{3}. Multiply \frac{k}{3} times \frac{2}{2}.

$$\frac{3\left(76-3r\right)}{6}-\frac{2k}{6}$$

Since \frac{3\left(76-3r\right)}{6} and \frac{2k}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(76-3r\right)-2k}{6}$$

Do the multiplications in 3\left(76-3r\right)-2k.

$$\frac{228-9r-2k}{6}$$

Factor

$$\frac{228-2k-9r}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{228-9r-2k}{6}$$

Consider 72-9r+63+93-2k. Multiply and combine like terms.

$$-9r-2k+228$$

Rewrite the complete factored expression.

$$\frac{-9r-2k+228}{6}$$