# Modulus/division **URL:** \ **Category:** ruby-talk\ **Created:** [18 February 2007 02:24 UTC](https://rubytalk.org/t/modulus-division/35461 "2007-02-18T02:24:22Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Derek\_Derek](https://avatars.discourse-cdn.com/v4/letter/d/6f9a4e/32.png) [@Derek\_Derek](https://rubytalk.org/u/Derek_Derek)\ **Post date:** [18 February 2007 02:24 UTC](https://rubytalk.org/t/modulus-division/35461/1 "2007-02-18T02:24:22Z")
hey guys, i am reading that "learning to program" by Chris Pine still and at the end of each lesson they give you a "give this a try" thing for you practice what you've learned... Anyway, at the end of Chapter 9 they give you this to try. I sort of have an idea of what i should do, but i really just don't understand the modulus(%) stuff, i was wondering if you guys could help me with just understanding what modulus is and how it works, thank you! BELOW IS THE PROBLEM THEY GIVE ... Old-school Roman numerals. In the early days of Roman numerals, the Romans didnÃÕ bother with any of this new-fangled subtraction IX nonsense. No sir, it was straight addition, biggest to littlest - so 9 was written VIIII, and so on. Write a method that, when passed an integer between 1 and 3000 (or so), returns a string containing the proper old-school Roman numeral. In other words, old\_roman\_numeral 4 should return 'IIII'. Make sure to test your method on a bunch of different numbers. Hint: Use the integer division and modulus methods on page 36. For reference, these are the values of the letters used: I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 > **···** > > -- > Posted via [http://www.ruby-forum.com/](http://www.ruby-forum.com/). ---
**Author:** ![Derek\_Perrault](https://avatars.discourse-cdn.com/v4/letter/d/f9ae1b/32.png) [@Derek\_Perrault](https://rubytalk.org/u/Derek_Perrault)\ **Post date:** [18 February 2007 02:49 UTC](https://rubytalk.org/t/modulus-division/35461/2 "2007-02-18T02:49:40Z")
Modulus division = Remainder division Two goes into five two times, with one left over. 5 / 2 = 2 (R1). Modulus division only returns that remainder. 5 % 2 = 1 Note that, when divided by 2, odd numbers always return 1, while even numbers always return 0. > **···** > > On 2/17/07, Derek Derek \ wrote: > > > hey guys, i am reading that "learning to program" by Chris Pine still > > and at the end of each lesson they give you a "give this a try" thing > > for you practice what you've learned... Anyway, at the end of Chapter 9 > > they give you this to try. I sort of have an idea of what i should do, > > but i really just don't understand the modulus(%) stuff, i was wondering > > if you guys could help me with just understanding what modulus is and > > how it works, thank you! > > > > BELOW IS THE PROBLEM THEY GIVE ... > > > > Old-school Roman numerals. In the early days of Roman numerals, > > the Romans didnÃÕ bother with any of this new-fangled subtraction > > IX nonsense. No sir, it was straight addition, biggest to littlest - > > so 9 was written VIIII, and so on. Write a method that, when > > passed an integer between 1 and 3000 (or so), returns a string > > containing the proper old-school Roman numeral. In other words, > > old\_roman\_numeral 4 should return 'IIII'. Make sure to test > > your method on a bunch of different numbers. Hint: Use the integer > > division and modulus methods on page 36. > > For reference, these are the values of the letters used: > > I = 1 V = 5 X = 10 L = 50 > > C = 100 D = 500 M = 1000 > > > > -- > > Posted via [http://www.ruby-forum.com/\](http://www.ruby-forum.com/%5C). ---
**Author:** ![Derek\_Derek](https://avatars.discourse-cdn.com/v4/letter/d/6f9a4e/32.png) [@Derek\_Derek](https://rubytalk.org/u/Derek_Derek)\ **Post date:** [18 February 2007 03:16 UTC](https://rubytalk.org/t/modulus-division/35461/3 "2007-02-18T03:16:28Z")
Derek Perrault wrote: > Modulus division = Remainder division > > Two goes into five two times, with one left over. 5 / 2 = 2 (R1). > Modulus division only returns that remainder. 5 % 2 = 1 > > Note that, when divided by 2, odd numbers always return 1, while even > numbers always return 0. okay, cool. i found the answer to the question on a forum online ... ANSWER: def old\_roman\_number input   while input \< 1 || input \> 3999     puts 'Please enter a number between 1 and 3999'     input = gets.chomp.to\_i   end   m\_mod = input%1000   d\_mod = input%500   c\_mod = input%100   l\_mod = input%50   x\_mod = input%10   v\_mod = input%5   m\_div = input/1000   d\_div = m\_mod/500   c\_div = d\_mod/100   l\_div = c\_mod/50   x\_div = l\_mod/10   v\_div = x\_mod/5   i\_div = v\_mod/1   m = 'M' \* m\_div   d = 'D' \* d\_div   c = 'C' \* c\_div   l = 'L' \* l\_div   x = 'X' \* x\_div   v = 'V' \* v\_div   i = 'I' \* i\_div   puts m + d + c + l + x + v + i end number = gets.chomp.to\_i old\_roman\_number(number) I understnad the first few lines .. the "while" stuff and and ending stuff too. do you think you explain to me why the % and / works here? i guess i really need to get better at math. i'm sorry if i'm being really stupid here, hah. i just want to really understand things, not just see and move on .. thank you again.. > **···** > > -- > Posted via [http://www.ruby-forum.com/\](http://www.ruby-forum.com/%5C). ---
**Author:** ![Jason\_Mayer](https://avatars.discourse-cdn.com/v4/letter/j/85e7bf/32.png) [@Jason\_Mayer](https://rubytalk.org/u/Jason_Mayer)\ **Post date:** [18 February 2007 05:00 UTC](https://rubytalk.org/t/modulus-division/35461/4 "2007-02-18T05:00:29Z")
I find that when I'm trying to understand what's going on, the best way to figure it out is to use IRB E:\Documents and Settings\Jason\>irb irb(main):001:0\> input = 3123 =\> 3123 irb(main):002:0\> m\_mod = input%1000 =\> 123 irb(main):003:0\> m\_div = input/1000 =\> 3 irb(main):004:0\> m = 'M' \* m\_div =\> "MMM" irb(main):006:0\> puts m MMM =\> nil irb(main):007:0\> You can probably figure out the rest from there. Hope that helps. > **···** > > On 2/17/07, Derek Teixeira \ wrote: > > > I understnad the first few lines .. the "while" stuff and and ending > > stuff too. do you think you explain to me why the % and / works here? i > > guess i really need to get better at math. i'm sorry if i'm being really > > stupid here, hah. i just want to really understand things, not just see > > and move on .. thank you again.. ---
**Author:** ![Sebastian\_Hungerecke](https://avatars.discourse-cdn.com/v4/letter/s/ba8739/32.png) [@Sebastian\_Hungerecke](https://rubytalk.org/u/Sebastian_Hungerecke)\ **Post date:** [18 February 2007 07:50 UTC](https://rubytalk.org/t/modulus-division/35461/5 "2007-02-18T07:50:07Z")
Derek Teixeira wrote: > okay, cool. i found the answer to the question on a forum online ... >   m\_mod = input%1000 Puts the remainder of division by 1000 (i.e. the three last digits of the number) in m\_mod. >   d\_mod = input%500 Remainder of division by 500 (i.e. the three last digits or if that number would be higher than 500, the three last digits minus 500) >   c\_mod = input%100 2 last digits. >   l\_mod = input%50 2 last digits minus 50 if necessary. >   x\_mod = input%10 Last digit. >   v\_mod = input%5 Last digit minus 5 if necessary. >   m\_div = input/1000 Divides the number by 1000, cutting of everything after the point (because this is integer division). So basically this returns everything but the three last digits. >   d\_div = m\_mod/500 This is one if the third to last digit (i.e. the one who specifies the hundreds) is 5 or higher and zero otherwise. >   c\_div = d\_mod/100 The third to last digit minus 5 if it's 5 or higher. >   l\_div = c\_mod/50 >   x\_div = l\_mod/10 >   v\_div = x\_mod/5 >   i\_div = v\_mod/1 The same thing for the second to last and last digit accordingly. > do you think you explain to me why the % and / works here? I hope this is what I just did and you understand it now. HTH, Sebastian Hungerecker > **···** > > -- > Ist so, weil ist so > Bleibt so, weil war so ---
**Author:** ![Derek\_Derek](https://avatars.discourse-cdn.com/v4/letter/d/6f9a4e/32.png) [@Derek\_Derek](https://rubytalk.org/u/Derek_Derek)\ **Post date:** [18 February 2007 13:46 UTC](https://rubytalk.org/t/modulus-division/35461/6 "2007-02-18T13:46:34Z")
i tried to get a better understanding of the % method, so i just set up a program to show me the results of the % of a number ... so i tried out the number 4. puts 4%1000 puts 4%500 puts 4%100 puts 4%50 puts 4%10 puts 4%5 and for everyline i got "4" as the remainder.. but when i tried these with a calulator .. i only got 4 as a remainder for the 1000. when i did the 4/500 i got a .008 .. so shouldn't the % be an 8? > **···** > > -- > Posted via [http://www.ruby-forum.com/](http://www.ruby-forum.com/). ---
**Author:** ![Sebastian\_Hungerecke](https://avatars.discourse-cdn.com/v4/letter/s/ba8739/32.png) [@Sebastian\_Hungerecke](https://rubytalk.org/u/Sebastian_Hungerecke)\ **Post date:** [18 February 2007 14:10 UTC](https://rubytalk.org/t/modulus-division/35461/7 "2007-02-18T14:10:10Z")
Derek Teixeira wrote: > and for everyline i got "4" as the remainder.. but when i tried these > with a calulator .. i only got 4 as a remainder for the 1000. when i did > the 4/500 i got a .008 .. so shouldn't the % be an 8? The remainder of divison has nothing to do with what would come after the decimal point. You can calculate x%y as follows: First you calculate x/y (cutting off everything after the decimal point). Then you take this number and substract it from x. For example: 421/100==4 4\*100==400 421%100==421-400==21 If y\>x then x/y==0, so x%y==x. HTH, Sebastian Hungerecker > **···** > > -- > NP: Nocte Obducta - Eins mit der Essenz der Nacht > Ist so, weil ist so > Bleibt so, weil war so ---
**Author:** ![Tim\_Hunter4](https://avatars.discourse-cdn.com/v4/letter/t/ea5d25/32.png) [@Tim\_Hunter4](https://rubytalk.org/u/Tim_Hunter4)\ **Post date:** [18 February 2007 14:14 UTC](https://rubytalk.org/t/modulus-division/35461/8 "2007-02-18T14:14:31Z")
Derek Teixeira wrote: > i tried to get a better understanding of the % method, so i just set up a program to show me the results of the % of a number ... > > so i tried out the number 4. > > puts 4%1000 > puts 4%500 > puts 4%100 > puts 4%50 > puts 4%10 > puts 4%5 > > and for everyline i got "4" as the remainder.. but when i tried these with a calulator .. i only got 4 as a remainder for the 1000. when i did the 4/500 i got a .008 .. so shouldn't the % be an 8? When I was in elementary school they taught us these words for division. Suppose you have 9 divided by 4. 4 is the "divisor". 9 is the "dividend". 4 goes into 9 2 times, so 2 is the "quotient", but since 4 times 2 is only 8, there is 1 left over. 1 is called the "remainder". The modulus operator returns the remainder after dividing two integers. That is, 9 % 4 = 1. So what is 4 % 5? 5 goes into 4 0 times. 0 times 5 is 0, so there is 4 left over. 4 % 5 = 4. For 4 % 10, 10 goes into 4 0 times, with 4 left over. 4 % 10 = 4. Same for 4 % 50 and all your other examples. For interesting experiments, use a divisor that is smaller than the dividend. 10 % 4 = 2. 12 % 3 = 0. For more interesting experiments, use negative numbers. ---
**Author:** ![Derek\_Derek](https://avatars.discourse-cdn.com/v4/letter/d/6f9a4e/32.png) [@Derek\_Derek](https://rubytalk.org/u/Derek_Derek)\ **Post date:** [18 February 2007 17:31 UTC](https://rubytalk.org/t/modulus-division/35461/9 "2007-02-18T17:31:14Z")
Timothy Hunter wrote: > Derek Teixeira wrote: > > > puts 4%5 > > > > and for everyline i got "4" as the remainder.. but when i tried these > > with a calulator .. i only got 4 as a remainder for the 1000. when i did > > the 4/500 i got a .008 .. so shouldn't the % be an 8? > > When I was in elementary school they taught us these words for division. > Suppose you have 9 divided by 4. 4 is the "divisor". 9 is the > "dividend". 4 goes into 9 2 times, so 2 is the "quotient", but since 4 > times 2 is only 8, there is 1 left over. 1 is called the "remainder". > The modulus operator returns the remainder after dividing two integers. > That is, 9 % 4 = 1. > > So what is 4 % 5? 5 goes into 4 0 times. 0 times 5 is 0, so there is 4 > left over. 4 % 5 = 4. For 4 % 10, 10 goes into 4 0 times, with 4 left > over. 4 % 10 = 4. Same for 4 % 50 and all your other examples. > > For interesting experiments, use a divisor that is smaller than the > dividend. 10 % 4 = 2. 12 % 3 = 0. > > For more interesting experiments, use negative numbers. i think i've got it! is this pretty mcuh what they are saying .. i put explanations next to each line .. def old\_roman\_number input   while input \< 1 || input \> 3999     puts 'Please enter a number between 1 and 3999'     input = gets.chomp.to\_i   end   m\_mod = input%1000 4/1000 means 1000 goes into 4 zero times so 0\*1000 = 0 .. so 4-0= 4   d\_mod = input%500 4/500 means 500 goes into 4 zero times 0\* 500 = 0 ... so 4-0=4   c\_mod = input%100 4/100 means 100 goes into 4 zero times 0\*100 =0 .. so 4-0=4   l\_mod = input%50 4/50 means 50 goes into 4 zero times 0\*50 = 0 .. so 4-0=4   x\_mod = input%10 4/10 means 10 goes into 4 zero times 0\*10 = 0 .. so 4-0 = 4   v\_mod = input%5 4/5 means 5 goes into 4 zero time 0\*5 = 0 .. so 4-0= 4   m\_div = input/1000 = 4/1000 = 0   d\_div = m\_mod/500 = 4/500 = 0   c\_div = d\_mod/100 = 4/100 = 0   l\_div = c\_mod/50 = 4/50 = 0   x\_div = l\_mod/10 = 4/10 = 0   v\_div = x\_mod/5 = 4/5 = 0   i\_div = v\_mod/1 = 4/1=4   m = 'M' \* m\_div = 0   d = 'D' \* d\_div = 0   c = 'C' \* c\_div = 0   l = 'L' \* l\_div = 0   x = 'X' \* x\_div = 0   v = 'V' \* v\_div = 0   i = 'I' \* i\_div = 4 \* I equals IIII   puts m + d + c + l + x + v + i end number = gets.chomp.to\_i old\_roman\_number(number) > **···** > > -- > Posted via [http://www.ruby-forum.com/\](http://www.ruby-forum.com/%5C). ---
**Author:** ![Edwin\_Fine](https://avatars.discourse-cdn.com/v4/letter/e/b3f665/32.png) [@Edwin\_Fine](https://rubytalk.org/u/Edwin_Fine)\ **Post date:** [18 February 2007 18:38 UTC](https://rubytalk.org/t/modulus-division/35461/10 "2007-02-18T18:38:06Z")
You can calculate modulus more expensively (but easier to understand) like this: def remainder(num, divided\_by)   num - (num / divided\_by).floor \* divided\_by end 'floor' effectively gets rid of everything past the decimal point and returns an integer. We know intuitively that if we divide 401 by 100, we get 4 remainder 1. Using the calculation (let's assume for laughs we have floating point numbers), 401.0 - (401.0 / 100.0).floor \* 100.0 = 401.0 - (4.01).floor \* 100.0 = 401.0 - 4 \* 100.0 = 401.0 - 400.0 = 1.0 remainder 401, 100 =\> 1 remainder 40, 100 =\> 40 remainder 123456, 87 =\> 3 remainder 123.45, 100.0 =\> 23.45 These values agree with the results of using '%'. Hope this helps. > **···** > > -- > Posted via [http://www.ruby-forum.com/](http://www.ruby-forum.com/).