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I'm studying a series on algorithms taught by "Abdul Bari" on youtube

Here is when he says "A into B" to talk about multiplying A by B

I know why some say "a times b" when talking about multiplication. I'm curious about the expression "a into b". Where might it come from?

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  • Here is a century-old attestation: books.google.com/…
    – user6726
    Commented Oct 9, 2019 at 17:01
  • It sounds all wrong to my ear, based on my experience with a variety of math instructors. Maybe it's a dialect thing. Commented Oct 10, 2019 at 6:06

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This is an archaism that survives in Indian English. When I learned the times tables in the 70s, this is how I did it: "1 into 1 is 1", "1 into 2 is 2" etc. We also were taught '4 by 2 is 2', with 'by' standing for division.

You can see 17th and 18th century references to this usage, e.g., 'for two into two is Four' (Henry More, 1712); 'for two into three is six' (Margaret Cavendish, 1668)

Meanwhile, you can see a similar use in a non-Indian example here.

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    It seems that "by" has also changed meaning as well. Do you have any idea why the word "into" might be used? Because the word "times" arises naturally when asking "how many times do I add the same number" when speaking about multiplication. But I can't find such an analog for "into" Commented Oct 10, 2019 at 11:56
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    The OED gives a meaning of 'into' as 'Used to indicate multiplication, as to multiply x into y (by considering the multiplicand replicated once for each unit of the multiplier).' Perhaps the verb 'multiply' got dropped over time? Commented Oct 10, 2019 at 12:25
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    That's weird. If you asked me "What is 2 into 6" I would say "3". Commented Oct 10, 2019 at 13:28
  • @DJClayworth So would I, in fact I would tend to think of both "into" and "by" as referring to division as in "2 into 6 is 3" and "8 by 2 is 4". I don't think I would use either of them but that is what I would understand.
    – BoldBen
    Commented Oct 18, 2019 at 12:58
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    I've noticed the "into" usage just recently in Indian English contexts and find it fascinating that "into" and "by" mean the opposite of what I'd expect. For me, something that is "6 by 3" would mean an area of 6 times 3, and "4 into 12" would mean "how many times does 4 go into 12", i.e., 12 divided by 4.
    – screwtop
    Commented Sep 14, 2022 at 5:49

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