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Primary education

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Original poster

Odd and even numbers

115 replies

user789653241 · 08/12/2017 22:08

Ds(9, yr5) asked me if decimal numbers can be defined as even or odd. I said no, but haven't got a clue why.

Can anyone give us some explanations please?

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sirfredfredgeorge · 09/12/2017 12:51

3 wouldn't be an integer then either though Barbara (since it could be the same expressed to 0)

I am actually interested to in why we particularly care about even/odd in school, it's of very limited use, we don't teach it as a general way of defining things about numbers is useful, it's taught as a fact, since that is all that it is.

Also, as we can see, lots of people don't understand it well, perhaps because they want it to be more meaningful and fundamental than just "we defined some rules"

sirfredfredgeorge · 09/12/2017 12:54

noblegiraffe I did also consider debating that, but 3.9recurring and 4 are just different ways of writing 4, they are equivalent both are simply transcriptions from the mathematical world. So given they are the same thing, you do have to say it is an integer.

SimultaneousEquation · 09/12/2017 12:57

I was not going to weigh in but saying “zero is not a number” is tantamount to climate change denial and spurious mmr autism links.

Take it from me (the username is a clue), or go and get a copy of the wonderful undergraduate text “Set Theory” by Enderton, that zero is a number, and indeed the number from which we derive all others.

noblegiraffe · 09/12/2017 13:00

sirfred but by that argument 0.2 is a fraction.

noblegiraffe · 09/12/2017 13:10

Thinking further, if we take any number that can be also written as a whole number to be an integer, then things like 12/4 are also integers.

Annorlunda5 · 09/12/2017 13:26

Snap

Thanks so much. So you don't get, say... 1.10 or 1.80 in the sense of '10' and '80', it's just 1.1 and then 1.8?

I am NOT looking forward to DDs maths homework, that's for sure!

noblegiraffe · 09/12/2017 13:38

am actually interested to in why we particularly care about even/odd in school

A number being even is a very useful property to have a shorthand for. If a number is even but not 2, you know instantly it's not prime. If you have an even numerator and denominator, you know that fraction (or ratio) can be simplified - obviously it might still be able to be simplified if not but it's a good first check. Is 1011 a term in the sequence 2, 6, 10, 14...? No because you can't get an odd by adding an even to an even. Multiply two evens and get an odd and you know you've gone wrong. It comes up all over the place.

TeenTimesTwo · 09/12/2017 13:41

Annor Don't worry, most of what has been discussed here won't really come up in any form of homework up to GCSE.
(Though it does sound to me as if you don't have a strong handle on the meaning of decimals so you may want to refresh that sometime.)

sirfredfredgeorge · 09/12/2017 13:46

If a number is threeit but not 3, you know instantly it's not prime, if you have a threeit numerator and denominator you know that it can be simplified, is 1011 a term in the sequence 3,9,15? No because you adding threeit's have to give a threeit etc.

Why is odd/even special cased over a threeit - sure it's a bit more useful (since the 2/3 non-threeit doesn't tell us as much as odd)

Changebagsandgladrags · 09/12/2017 13:54

With threeit you have more numbers that are not threeit than are threeit.

So if a number is not threeit, it could be prime. But from 1 -10 there is 1, 2, 4, 5, 7, 8 to check. Up to twenty even more...You're only knocking out a third of the numbers

With not even there's less to check 1, 3, 5, 7, 9 as you're knocking out half to start with

noblegiraffe · 09/12/2017 13:55

sirfred threeit is less useful because a threeit comes up less often and also because it's much harder to identify a number by sight as a threeit than an even (obviously you can do the adding the digits trick which means 1011 is a threeit but still not necessarily in that sequence because you are adding 6 not 3 unless you also consider whether it is even or odd).

noblegiraffe · 09/12/2017 13:58

...meaning 1011 is a term in the sequence 3,9,15...

TeenTimesTwo · 09/12/2017 13:59

This is why I like MN.

Changebagsandgladrags · 09/12/2017 14:00

Yes a threeit can end in a 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9 not easy to identify
..

noblegiraffe · 09/12/2017 14:04

I'm trying not to swear, Teen

TeenTimesTwo · 09/12/2017 14:09

cantkeepawayforever · 09/12/2017 14:11

Noble, is it the Americans who call 0.2 a decimal fraction? I know I have come across it when searching for resources.

OhYouBadBadKitten · 09/12/2017 14:28

dd agrees that 3.99999999 is an integer, but says we would be stupid to use it.
I feel the differences between a mathematician and an engineer causing a family rift.

noblegiraffe · 09/12/2017 14:32

I thought 2/10 was a decimal fraction (or 21/100 or 457/1000) as it's a fraction with a denominator which is a power of 10. They can be easily written as decimals, but numbers which have a decimal representation can't always be written as decimal fractions (e.g recurring decimals/irrational numbers).
My take would be 0.2 can be written as a decimal fraction, but it's also equal to 1/5 which is not a decimal fraction. Calling 0.2 a decimal fraction seems a bit muddled to me!

noblegiraffe · 09/12/2017 14:34

dd agrees that 3.99999999 is an integer

Ooh ask her if she thinks 0.2 is a fraction

OhYouBadBadKitten · 09/12/2017 15:14

when I get a chance I’ll ask her noble.

catkind · 09/12/2017 16:03

Hmm, 3.9 recurring is equal to 4 and 4 is an integer but I'd be reluctant to classify 3.9 recurring as an integer. It feels like saying that 0.2 is equal to 1/5 and 1/5 is a fraction so 0.2 is a fraction.

"Is a fraction" is not really the same sort of description as "is an integer" though. The integers are a well defined subset of the real numbers. Any given number either is or isn't in that subset, regardless of how you represent it. It's more comparable to rational numbers like that. 0.2 is represented as a decimal but it is still a rational number. The square root of 2 is not a rational number or an integer, but you can't just assume that from the way it's represented, you have to prove it isn't.

"Fraction" also has other usages, I've heard it used for any number that isn't an integer, or also for any number between 0 and 1, or any expression written as a/b for any kind of a and b not just integers. So I'd be cautious about using "is a fraction/isn't a fraction" without specifying further what I mean. e.g. I'd say a rational number is a number which can be expressed as a simple fraction a/b where a and b are integers and b is nonzero 0.

catkind · 09/12/2017 16:04

Oops extra 0 sneaked in at the end there.

noblegiraffe · 09/12/2017 16:32

The integers are a well defined subset of the real numbers. Any given number either is or isn't in that subset, regardless of how you represent it.

Obviously some labels apply to any representation, such as ‘surd’ - however it’s written it still can’t be written as a fraction. But other labels don’t, like ‘decimal fraction’. Are you sure that ‘integer’ does? Does it really apply to 4.0 when 4.0 may represent the integer 4, but may also represent a range of numbers rounded to 2s.f.?

Original poster

user789653241 · 09/12/2017 16:39

Thank you everyone for your help.
Here's comment from my ds below.

Thank you everybody. I now get how decimals can't be even or odd.

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