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Let's define the first number as "ab" and the second number as "cd". In "ab"-"cd" proces, if "b" is smaller than "d", we add 10 to "b" and reduce 1 from "a".

In Turkish, we called it "taking a tenner from neighbour". How do you use that term in English?

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In English, a tenner is an informal word for a £10 note. See dictionary.cambridge.org/dictionary/british/tenner?q=tenner –  Tristan Jun 29 '13 at 16:43
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This might be better asked on Math.SE or a specialist teaching forum. You're describing the Decomposition method of subtraction, but I don't think there's a formal way of expressing how that is carried out. When I was at school we used to say borrow one from here which makes ten in this column. I rather like "take a tenner from a neighbour"! –  Andrew Leach Jun 29 '13 at 17:00
    
I am completely baffled by this question, would you be so kind as to explain it using simpler language so that I might understand –  xxx Jun 29 '13 at 20:35
    
Yes - decomposition. For instance, 47 - 23 = 24, no problem (we're using the usual algorithm, 7 - 3, and then 4 - 2 in the tens column): (40 + 7) - (20 + 3) But what about 54 - 28 = ? The problem is that 8 can't be subtracted from 4 using only positive numbers. So, we recognise that 54 - 28 = (40 + 14) - (20 + 8) and now we can handle the units (14 - 8 = 6) and then the resulting tens (40 - 20) Instead of regarding 54 the obvious way (50 + 4), we've decomposed the 50 into 40 + 10, transferring a ten from the tens to the units. –  Edwin Ashworth Jun 29 '13 at 22:44
    
A great deal of the confusion in mathematics education arose when teachers talked about the decomposition method without explaining to parents that it was what they had learned as borrow and pay back. –  Fortiter Jun 29 '13 at 23:40

1 Answer 1

up vote 3 down vote accepted

In English this is called borrowing:

32 − 15
= (20 + 12) − (10 + 5)
“borrow the 1”
= (20 − 10) + (12 − 5)
= 10 + 7
= 17

Going the other direction, as in addition, is called carrying:

25 + 39
= (20 + 5) + (30 + 9)
= (20 + 30) + (5 + 9)
= (20 + 30) + 14
“carry the 1”
= (20 + 30 + 10) + 4
= 60 + 4
= 64

Both are special cases of regrouping.

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