Q. What is the remainder of (20*27) when it is divided by 25?

Note: Rof = remainder of

A.

**The formula**I used is: Rof xy/n = Rof {Rof[(x-n)/n] * Rof[(y-n)/n]} / n

Therefore, Rof 20*27/25 = Rof {Rof[(20-25)/25] * Rof[(27-25)/25]} / 25

= Rof {Rof[(-5)/25] * Rof[2/25]} / 25

= Rof [(-5 * 2) / 25]

= Rof [(-10) / 25]

= (-10)

But,

**since the remainder is negative, we add n to it to give us the remainder.**

Therefore, Rof 20*27/25 = -10 + n = -10 + 25 = 15.

**Why did we add n to the negative remainder?**
## 2 comments:

First lets solve this problem differently:

20*27/25

There is a rule that says

R[pq/x] = R[p/x]*R[q/x]

1. R[20/25]*R[27/25]

First divide 27 by 25. Rem=2

2. We are left with:

R[20/25]*R[2/25] = R[20*2/25]

--using inverse of the rule mentioned above

3. Now find R[40/25], your answer is 15.

Look you can also solve this using -ve remainder rule. Let me know if that is wht you need.

I'm aware of the formula you gave. But I used this formula on purpose, to get a negative remainder, and thus bring out my doubt so as to why we add the divisor to the remainder when it is negative.

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