SOLUTION: 9. a) How many different numbers, including zero, can there be as remainders if 19 is divided into 2? Am I supposed to know how to find this, or do I need to divide it out? If t

Question 198684This question is from textbook Elementary Algebra
: 9. a) How many different numbers, including zero, can there be as remainders if 19 is divided into 2?
Am I supposed to know how to find this, or do I need to divide it out? If there is a way to find it without dividing it out, can you show me how?
Thanks. This question is from textbook Elementary Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Well let's divide some numbers into 2 to see what possible remainders we get

0: 0/2 = 0 remainder 0
1: 1/2 = 0 remainder 1
2: 2/2 = 1 remainder 0
3: 3/2 = 1 remainder 1
4: 4/2 = 2 remainder 0
5: 5/2 = 2 remainder 1
6: 6/2 = 3 remainder 0

etc...

Starting to see the pattern? It turns out that if the dividend (ie the numerator) is even, then the remainder is 0. Otherwise, if the dividend is odd, then the remainder is 1. So the only possible choices of remainders are 0 and 1. These are the ONLY two possible choices.

So because 19 is odd, this means that the remainder of dividing 19 into 2 gets you a remainder of 1.

So if you did the above work in a previous exercise, then you wouldn't have to do any dividing, but it helps see what's going on.
RELATED QUESTIONS
I am being asked to graph: 4x^2-y^2>36 So i know that it is going to be a hyperbola,... (answered by Mathtut)

I am being asked to graph: 4x^2-y^2>36 So i know that it is going to be a hyperbola,... (answered by Mathtut)

The internal telephone numbers in the phone system on a campus consist of five digits... (answered by mathie123)

I don't know if this is the right section because I don't know the name of what I am... (answered by solver91311,jim_thompson5910)

there are 3 numbers in a locker combination :19, 22 and 28. In how many different ways... (answered by gargituli)

While playing mini golf, you hit the ball off of a wall to attempt at making it in the... (answered by Boreal,greenestamps)

There is a circle divided into 3 parts, one part is 3/4, one part is 1/3 and we are asked (answered by solver91311)

I am not that strong in this field. Can you look over this stuff AND get me the answers... (answered by Alan3354)

I need your help here-please 14. (2 pts) How many different ways are there for an... (answered by jim_thompson5910,josmiceli)