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 July 9th, 2017, 12:03 AM #1 Newbie   Joined: Jul 2017 From: pakistan Posts: 3 Thanks: 0 Complete divisor of a number Hi all, I am having such a naïve problem, yet unable to comprehend it now: $\displaystyle 21904/2$ should come out to be $\displaystyle 1952$ plainly, but calculator suggests it to be $\displaystyle 10952$. What's the rule here? Last edited by skipjack; July 9th, 2017 at 01:07 AM.
 July 9th, 2017, 12:25 AM #2 Newbie   Joined: May 2017 From: California Posts: 15 Thanks: 1 If 21904/2 = 1952, then 1952(2) = 21904, but that isn't true. 21904 / 2 = 10952 is true though because 21904 = 10952(2). I think you may have forgot a 0 somewhere in your solution, because 1952 and 10952 are similar-looking. Last edited by skipjack; July 9th, 2017 at 01:07 AM.
July 9th, 2017, 05:42 AM   #3
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Quote:
 Originally Posted by Choboy11 If 21904/2 = 1952, then 1952(2) = 21904, but that isn't true. 21904 / 2 = 10952 is true though because 21904 = 10952(2). I think you may have forgot a 0 somewhere in your solution, because 1952 and 10952 are similar-looking.
Sorry, what I am asking is the reason for "ZERO" in quotient in below image at link provided.
What's the rule for it?
Why "Zero" comes in quotient while there isn't a need? - Album on Imgur

Last edited by skipjack; July 9th, 2017 at 06:04 AM.

 July 9th, 2017, 06:11 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,288 Thanks: 1968 There is a need. When 1 and 9 are brought down, the 0 is because the 1 isn't large enough to have a non-zero multiple of 2 subtracted from it. Subtracting a zero multiple of 2 is omitted (as subtracting zero has no effect), but 0 has to be entered in the quotient.
July 9th, 2017, 06:17 AM   #5
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Quote:
 Originally Posted by skipjack Subtracting a zero multiple of 2 is omitted (as subtracting zero has no effect), but 0 has to be entered in the quotient.
So,what you mean is : It's true for all such cases where zero multiple of a'n' is omitted e.g. for 3,4,5 etc?

 July 9th, 2017, 10:48 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,964 Thanks: 991 4 divided by 7 = 0 remainder 4 May I ask: are you serious? Thanks from Jeddi
 July 29th, 2017, 05:04 AM #7 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 Long division is typically taught in fourth or fifth grade, to 9 or 10 year olds. Of course, we have no way of knowing how old you are.
July 29th, 2017, 01:42 PM   #8
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Quote:
 Originally Posted by Jeddi Sorry, what I am asking is the reason for "ZERO" in quotient in below image at link provided. What's the rule for it? Why "Zero" comes in quotient while there isn't a need? - Album on Imgur
The zero comes in because

$20000 < 21904 < 22000 \implies$

$\dfrac{20000}{2} < \dfrac{21904}{2} < \dfrac{22000}{2} \implies$

$10000 < \dfrac{21904}{2} < 11000.$

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