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

 January 31st, 2018, 04:44 PM #1 Newbie   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. Thanks. January 31st, 2018, 05:21 PM #2 Senior Member   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 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. Tags divison, integer, positive, remainder Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Singi Real Analysis 1 March 19th, 2017 01:27 PM TobiWan Algebra 13 November 25th, 2016 05:52 AM John Travolski Algebra 6 March 16th, 2016 05:23 PM Alann Number Theory 7 November 7th, 2012 08:39 AM K Sengupta Number Theory 6 March 18th, 2009 04:13 PM

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