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When someone says "two times three', which do you imagine, 3+3 or 2+2+2?

When someone says "multiply two by three, which do you imagine, 3+3 or 2+2+2?

The results are the same, but the concept may be different.


I think I need more explanation about this question. When you see 2x3, you would probably say two times three or multiplying two by three. Multiplying two by three means 2+2+2. Then, why do you say two times three for 2x3?


I'm not sure that this is off topic. I would like to know what "two times three" means as a language. Does it mean 3+3? If so, why do you say two times three when you read 2x3? I feel 2x3 means three times two as you say 2 multiplied by 3 to read 2x3.

I am not interested in the Math logic.

  • 2
    I think this is more a question for an educational psychologist, than for an English language forum. – WS2 Oct 27 '14 at 7:30
  • @WS2 Maybe you are right. But I am interested in the usages of these words and phrases. – 243 Oct 27 '14 at 7:36
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    The question is POB, not about English. Multiplying two times three is 3+3, then why do you say 2+2+2? – Canis Lupus Oct 27 '14 at 8:19
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    Whatever I might have been taught as a child, I see absolutely nothing. I can manipulate them just fine, but there's no intuition informing me that 2x3 is different from 3x2. I can visualize a rectangle, one orientation or another, but that never comes up when I am manipulating factors. – Mitch Oct 27 '14 at 12:53
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    I imagine 6. – Oldcat Oct 27 '14 at 18:49
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This is actually possible to answer, by looking at how we use both "times two" ("times three", "times four", etc.) as a standalone phrase to multiply whatever comes before it and "two times" ("three times", "four times", etc.) as a standalone phrase to multiply whatever comes after it.

Here are a few cites from the Corpus of Contemporary American English:

  • Do you know what it's like to have triplets? It's just everything times three: three pairs of grubby little hands, smearing food all over your brand new Chihuahua outfits; three pairs of feet in their weird, soft little shoes; three pairs of eyes, brown, like my husband's.

  • Iran is a much larger country, geographically, than Iraq. It has three times the population

  • There was no way she was going to have to pay $333 an hour, times three, for having sex with this guy.

  • At stake are 518 delegates, more than three times the number awarded so far in the unpredictable competition

  • New paint. New furniture. All those special touches for a new baby times three.

  • a mostly Athenian army crushed a veteran Persian force three times its size

  • — The 88 keys were taking over the family.
    — That is a true statement. I mean, literally, because it wasn't 88 keys. It was 88 times two, times three, times four, and eventually times five.
    — Five grand pianos in the house?
    — Yes.

  • LED can run two to three times the cost of conventional lighting sources

  • The next month you write three $100 checks and put each into an envelope that asks only for $50, and now you feel as if you had real money, savings, like you've spent $50 and saved $50, as if you have $50 to spend, and that's times three.

  • Mercury times three
    In three flybys, MESSENGER snaps portraits of portions of Mercury[.]

  • And they suffered nearly three times the number of wounded

  • Nefertiti Times Three

  • I saw a knife, a guy that was probably three times the size of my dad

  • After "Sleep tight, sweetie" times three, Jonah and I were rarely finished being parents.

  • FUNAI patrols 54,000 square miles of remote territory, an area more than three times the size of Switzerland

  • I could sense what other people were feeling three times as deeply as other kids, and my reactions would be times three. [Lo and behold — both variants in the same sentence!]

There are many more, but you get the drift.

If "A times B" had only one possible parse tree, only one of the two variants would be productive, and so half the above quotes would be ungrammatical, and indeed nonexistent. But they are all there and they are all fine, which goes to show that multiplication is commutative not only in maths, but also in the English language.

TL;DR: Sometimes, in "A times B", the "times B" part is considered to be a single unit, other times it's the "A times". Both readings are possible and productive, and often enough, you can even use them completely interchangeably without restructuring anything. You can patrol an area three times the size of Switzerland, and you can patrol an area the size of Switzerland times three.

So a 2×3 is a 2+2+2 is a 3+3.

Edit: It is important to note that this is not universally true of all languages. For example, in Russian, "three times two" can only be parsed as "[three times] two"; the parsing "three [times two]" is impossible. So wondering how English handles this is indeed a valid question, and indeed one about English rather than about how the human brain generally works.

  • So the fact that multiplication is commutative has suffused into the language. – Peter Shor Oct 27 '14 at 16:27
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    @PeterShor: yes, and I should add that this is not universally true of all languages. In fact I will edit the answer to elaborate on that. – RegDwigнt Oct 27 '14 at 20:36
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Since this is a question about grammatical patterns and not math, we can look at how the numbers are arranged in other patterns.

There are the alternate patterns 'twice three' and 'two threes' which sound like 3+3.

How many threes do you have?

I have two of them, I have two threes.

This would correspond to a list of threes that has two of them 3+3.

But this is forcing logic on something that is just an idiom of language. Two times three is just a rectangle of 2 by 3. Which is one is across and which is down really doesn't come into the explicit meaning of it. In practical usage, whether you say '$3.79 times 4' or '4 times $3.79' doesn't change anything and people will say either.

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Obviuosly, "times" indicates the iterations.

two times three

The qty./no.: 3
no. of iterations: 2
3 + 3

(Multiply two)( by three)

(2) (x 3)
There's no serial addition.
HTH.

  • Thank you. I thought so, but when you see 2x3, you would probably say two times three or multiplying two by three. Multiplying two by three means 2+2+2. That's what I thought. – 243 Oct 27 '14 at 7:40
  • You are right, too. We are accustomed to reading the 'x' as 'times,' thus inverting the order: (2)( times 3 i.e., 3 times) – Kris Oct 27 '14 at 7:51
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two times three = two, times three = two, three times = two, two, two

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