Solve r+2/3-11/6-31/2r

$$r + \frac { 2 } { 3 } - 1 \frac { 1 } { 6 } - 3 \frac { 1 } { 2 } r$$

Evaluate

$$\frac{-5r-1}{2}$$

Solution Steps

Multiply 1 and 6 to get 6.

$$r+\frac{2}{3}-\frac{6+1}{6}-\frac{3\times 2+1}{2}r$$

Add 6 and 1 to get 7.

$$r+\frac{2}{3}-\frac{7}{6}-\frac{3\times 2+1}{2}r$$

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

$$r+\frac{4}{6}-\frac{7}{6}-\frac{3\times 2+1}{2}r$$

Since \frac{4}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$r+\frac{4-7}{6}-\frac{3\times 2+1}{2}r$$

Subtract 7 from 4 to get -3.

$$r+\frac{-3}{6}-\frac{3\times 2+1}{2}r$$

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

$$r-\frac{1}{2}-\frac{3\times 2+1}{2}r$$

Multiply 3 and 2 to get 6.

$$r-\frac{1}{2}-\frac{6+1}{2}r$$

Add 6 and 1 to get 7.

$$r-\frac{1}{2}-\frac{7}{2}r$$

Combine r and -\frac{7}{2}r to get -\frac{5}{2}r.

$$-\frac{5}{2}r-\frac{1}{2}$$

Expand

$$\frac{-5r-1}{2}$$

Solution Steps

Multiply 1 and 6 to get 6.

$$r+\frac{2}{3}-\frac{6+1}{6}-\frac{3\times 2+1}{2}r$$

Add 6 and 1 to get 7.

$$r+\frac{2}{3}-\frac{7}{6}-\frac{3\times 2+1}{2}r$$

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

$$r+\frac{4}{6}-\frac{7}{6}-\frac{3\times 2+1}{2}r$$

Since \frac{4}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$r+\frac{4-7}{6}-\frac{3\times 2+1}{2}r$$

Subtract 7 from 4 to get -3.

$$r+\frac{-3}{6}-\frac{3\times 2+1}{2}r$$

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

$$r-\frac{1}{2}-\frac{3\times 2+1}{2}r$$

Multiply 3 and 2 to get 6.

$$r-\frac{1}{2}-\frac{6+1}{2}r$$

Add 6 and 1 to get 7.

$$r-\frac{1}{2}-\frac{7}{2}r$$

Combine r and -\frac{7}{2}r to get -\frac{5}{2}r.

$$-\frac{5}{2}r-\frac{1}{2}$$