1
$\begingroup$

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 $a= \overbrace{(b+1)}^{q}\cdot 7+\overbrace{3}^{r}$

$\endgroup$
1
  • $\begingroup$ the remainder must be less than the divider $\endgroup$
    – J. Yu
    Mar 5 '16 at 13:06
0
$\begingroup$

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 $a=7*b+7+3=7*b+10$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.