My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

Thanks Tree2Thanks
  • 1 Post By romsek
  • 1 Post By Country Boy
LinkBack Thread Tools Display Modes
January 31st, 2018, 04:44 PM   #1
Joined: Jan 2018
From: Toronto

Posts: 12
Thanks: 0

Divison - Remainder of Positive Integer

The remainder of any positive integer when divided by 100 is the integer made of the two rightmost digits - True or False and why?

- I am unsure how to answer this question. I say true, but don't know how to answer the why. Any suggestions on how two answer that question is greatly appreciated.

Tricia is offline  
January 31st, 2018, 05:21 PM   #2
Senior Member
romsek's Avatar
Joined: Sep 2015
From: USA

Posts: 2,549
Thanks: 1399

any positive integer can be written as

$i = 100k + r,~0 \leq r < 100$

so clearly $\dfrac{i}{100} = r$

$r$ is the rightmost two digits
Thanks from Tricia
romsek is online now  
February 1st, 2018, 03:31 AM   #3
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Ooh, I just cannot look at "$\displaystyle \frac{i}{100}= r$" without cringing!

What you mean, of course, is that is i= 100k+ r then $\displaystyle \frac{i}{r}= \frac{100k+ r}{100}= k+ \frac{r}{100}$ so that the remainder is r.

Tricia, do you understand that our numeration system is "base 10"? That is that the number "3215" means $\displaystyle 3\times 10^3+ 2\times 10^2+ 1\times 10+ 5= 3 \times 1000+ 2\times 100+ 1 \times 10+ 5= (3\times 10+ 2)\times 100+ 1\times 10+ 5$.

If we divide by 100, that "100" cancels the "100" I factored out of the first two digits leaving a quotient of $\displaystyle 3\times 10+ 2= 32$ and a remainder of $\displaystyle 1\times 10+ 5= 15$, the last two digits.
Thanks from Tricia

Last edited by Country Boy; February 1st, 2018 at 03:37 AM.
Country Boy is offline  

  My Math Forum > High School Math Forum > Elementary Math

divison, integer, positive, remainder

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
prove that there exist m, positive integer Singi Real Analysis 1 March 19th, 2017 01:27 PM
For a fixed positive integer n consider the equation TobiWan Algebra 13 November 25th, 2016 05:52 AM
Find the Smallest Positive Integer that... John Travolski Algebra 6 March 16th, 2016 05:23 PM
Smallest positive integer... Alann Number Theory 7 November 7th, 2012 08:39 AM
Positive Integer Exponent Pair Puzzle K Sengupta Number Theory 6 March 18th, 2009 04:13 PM

Copyright © 2019 My Math Forum. All rights reserved.