# Find the remainder and quotient when we will divide $a$ by $q$

When we divide $a$ by $b$ we get remainder $r=10$ and quotient $q=7$

What will be the remainder and quotient when we will divide $a$ by $q$?

My attempt:

$$a=b\cdot \overbrace{7}^{q}+\overbrace{10}^{r}\Longrightarrow a= \overbrace{b}^{q}\cdot 7+\overbrace{10}^{r}$$

The quotient is $b$ and the remainder will be $10$

But I don't understand why the answer should be $a= \overbrace{(b+1)}^{q}\cdot 7+\overbrace{3}^{r}$

• the remainder must be less than the divider Mar 5 '16 at 13:06

Well, we know $|7*b|<|a|$, so $7$ goes into $a$ at least $b$ times. But$7$ also goes into $10$ an additional time. Multiplying out $a=(b+1)*7+3$, we have $a=7*b+7+3=7*b+10$.