Simplify (13-3/2r)-(1-r)

$(13 - \frac{3}{2} r) - (1 - r)$

Step 1

Simplify each term.

Combine $r$ and $\frac{3}{2}$ .

$13 - \frac{r \cdot 3}{2} - (1 - r)$

Move $3$ to the left of $r$ .

$13 - \frac{3 \cdot r}{2} - (1 - r)$

Apply the distributive property.

$13 - \frac{3 r}{2} - 1 \cdot 1 - - r$

Multiply $- 1$ by $1$ .

$13 - \frac{3 r}{2} - 1 - - r$

Multiply $- - r$ .

Multiply $- 1$ by $- 1$ .

$13 - \frac{3 r}{2} - 1 + 1 r$

Multiply $r$ by $1$ .

$13 - \frac{3 r}{2} - 1 + r$

Step 2

Subtract $1$ from $13$ .

$- \frac{3 r}{2} + 12 + r$

Step 3

To write $r$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 r}{2} + r \cdot \frac{2}{2} + 12$

Step 4

Combine $r$ and $\frac{2}{2}$ .

$- \frac{3 r}{2} + \frac{r \cdot 2}{2} + 12$

Step 5

Combine the numerators over the common denominator.

$\frac{- 3 r + r \cdot 2}{2} + 12$

Step 6

Add $- 3 r$ and $r \cdot 2$ .

Reorder $r$ and $2$ .

$\frac{- 3 r + 2 \cdot r}{2} + 12$

Add $- 3 r$ and $2 \cdot r$ .

$\frac{- r}{2} + 12$

Step 7

Move the negative in front of the fraction.

$- \frac{r}{2} + 12$