Question 1208362: The math subtraction problem.
210,290
- 45,720
= 164,570 (I need to know why did the zero next to the 1
was changed to the number 9 in order to subtract
the number 5).
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
For this technique, see these sources and learn from them
video lesson (Youtube)
https://www.youtube.com/watch?v=1GazztzsIuY
textual lesson
https://www.houseofmath.com/encyclopedia/numbers-and-quantities/arithmetic/addition-and-subtraction/how-to-subtract-using-the-column-method
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Comment from student: Thank you for instructing me to click on Youtube to learn about how to explain the subtraction problem. I truly appreciate you.
My response: It is a strange and unnatural form to express your gratitude. I would even say - a miserable form.
I did not instruct you to click on Youtube.
I simply found appropriate and easy accessible sources for you in the internet, and if you want to say "Thanks",
say it exactly in this form: "Thank you for finding/pointing appropriate sources for me to learn the subject from".
In the form as you write your comment, it is, probably, a form to troll - not a form to gratitude.
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
That's a great question. Many people do not know why, because elementary
teachers often just say "You do it because it works", or "because I said so"!
In short, it's not 9 you're changing the 0 to. You're adding 90 because that
digit is in the placeholder for 10 times as much as the digit you're borrowing
it for. When you can't borrow from the digit next door on the left, and have to
borrow from two doors on the left, you borrow 100 instead of 10, so you dump the
extra 90 that you didn't need to borrow on the zero that you couldn't borrow
from.
When you have to borrow from three doors over, you borrow 1000, which is
borrowing 990 too much, so you dump 900 on the zero 2 doors over and 90 on the
digit next door and add the remaining 10 to the digit you're borrowing it for.
The number of units (one, ten, hundreds, thousands, ten-thousands, etc.)
which each digit tells how many of -- is always 10 times as much as how many
units the digit just right of it tells how many of.
Normally when subtracting by hand, when the upper digit is smaller than the
lower digit, we borrow 1 of the units from the digit just to the left of it,
which is actually 10 units, and add 10 to the digit that was too small to
subtract from, and then we reduce the digit just to the left by 1.
But sometimes the digit to the left is 0 and we can't borrow 10 from it.
So we must go to the next digit to the left, and borrow 100 from it instead
of 10 from the one next door. So we have over-borrowed.
We only wanted to borrow 10 units, not 100 units, so we need to get rid of
the extra 90 that we borrowed.
So we get rid of the extra 90 we borrowed by changing the digit (0) we couldn't
borrow 10 from, to a 9. (It's really adding 90 to it because the units count 10
times as much.) Then we take the remaining 10 and add it to the digit that was
too small to subtract from.
Recap: We couldn't borrow 1 of the units from the digit just to the left (which
would have been 10 of the units you needed) because it was 0. So we borrowed 1
from the next digit to the left (which is 100 of the units we needed to borrow).
We only needed to borrow 10, but we had to borrow 100 instead. So we borrowed
90 too much. So to get rid of the extra 90 units we borrowed, we added 9 to the
0 we couldn't borrow from. Since that digit tells 10 times as many units as
the digit we needed the 10 for, changing the 0 to 9 amounts to getting rid
of the extra 90 we borrowed.
Read what I wrote several times. You'll get it.
[I heard that some third grade teacher told their students "You change it to 9
because you feel sorry for that placeholder since it only had 0. So you give it
as much as you can to cheer it up, which is 9" LOL]
Edwin
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