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 2×3, 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 2×3?
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 2×3? I feel 2×3 means three times two as you say 2 multiplied by 3 to read 2×3.
I am not interested in the Math logic.
Best Answer
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:
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.