Solve for q a=qb+r

$a = q b + r$

Rewrite the equation as $q b + r = a$ .

$q b + r = a$

Subtract $r$ from both sides of the equation.

$q b = a - r$

Divide each term in $q b = a - r$ by $b$ and simplify.

Divide each term in $q b = a - r$ by $b$ .

$\frac{q b}{b} = \frac{a}{b} + \frac{- r}{b}$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{q b}{b} = \frac{a}{b} + \frac{- r}{b}$

Divide $q$ by $1$ .

$q = \frac{a}{b} + \frac{- r}{b}$

Simplify the right side.

Move the negative in front of the fraction.

$q = \frac{a}{b} - \frac{r}{b}$