What is the quotient and remainder when dividing -5 by 3?

[EKS]

I just learned something kind of interesting.

What is the quotient and remainder when dividing -5 by 3?  

[QueenCat]

-1.66666666667

[wathe]

-2 R1, I think.

dividend = divisor * quotient + remainder

-5 = 3(-2)+1

(It's been a while since I've had to think about this!)

Edited January 3 by wathe

[EKS]

14 minutes ago, wathe said:

-2 R1, I think.

dividend = divisor * quotient + remainder

-5 = 3(-2)+1

(It's been a while since I've had to think about this!)

That's right!  The remainder is positive.  

I'm pretty sure that in all of the elementary math materials we used, we never encountered this.  I think it must be because negative number division is typically introduced after kids stop dealing with remainders.

I just learned this from my abstract algebra text.

[maize]

Why is it done this way? 

[City Mouse]

This doesn’t generally come up in elementary math because division with remainders is only taught through 4th or maybe early 5th grade. By the time division with negative numbers is introduced, students are diving to decimals rather than remainders.

[EKS]

5 minutes ago, maize said:

Why is it done this way? 

Convention--though a google search makes me think that it sometimes changes depending on the application.

 

[Ausmumof3]

So can it not also be -1 remainder -2 or is that just not how it’s done? Because if we divided into a fraction it would be -1 2/3 not -2 and positive 1/3?

I’ve never come across this before.

[Drama Llama]

1 hour ago, EKS said:

Convention--though a google search makes me think that it sometimes changes depending on the application.

 

I have never seen remainders used in a math problem for kids who are far enough along to be working with negative numbers, unless there's a context.  But if there's a context, then you need to use the context to understand whether a positive or negative remainder makes sense.