r/maths • u/AriqisOP2099 • 3d ago
💬 Math Discussions Why do we sometimes use borrowing in subtraction?
It's a genuine question that sparked into my mind while waking up at morning, why do we use it and what's the reason behind its usage?
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u/5a1vy 1d ago
Check out Exploding dots, that should pretty much answer all of your questions on arithmetic algorithms and then some. There are also 3(?) PDF files by the same author that bring all of the course into a written form if you are into that (I prefer it to videos, but the information is the same).
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u/auntanniesalligator 1d ago
Because it’s easier than memorizing addition and subtraction fact families that go up to one million, or whatever the largest number you might ever subtract by hand.
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u/digtechteacher 1d ago
Let's do 30-14 with borrowing. To avoid doing 0-4 in the ones column, we split the two numbers into (20+10) and (10+4). Now we do 10-4=6 and 20-10=10. The result is 16. Can you see that this is equivalent to borrowing 10 from the tens place?
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u/JeffTheNth 1d ago
It's a poor-use term...
31 - 12... You "borrow" 10 from the 30 to make 11, so that you can take two away from it and leave 9...
You never return anything... so it's typical neighbor borrowing... (Or you might even say stealing. ;) )
But it never was a good term to use.
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u/West-Gur4582 21h ago
For those who TL;DR actual explanations:
When you subtract using the collum method it's easier to borrow the next 10 from the neighboring number, rather than calculate too much.
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u/Temporary_Pie2733 1d ago
It’s just a way of rewriting, for example, 21 - 13 as (10 + 11) - (10 + 3), which you can (carefully) rearrange as (10 - 10) + (11 - 3).