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# Worked example: Subtracting 3-digit numbers (regrouping)

Learn to use regrouping (borrowing) and place value to subtract 971-659. Created by Sal Khan.

Video transcript

Let's try to subtract
659 from 971. And as soon as you start trying
to do it, you face a problem. You go to the ones
place, and you say, how am I going to
subtract a 9 from a 1? And the answer lies in
regrouping, taking value from one of the other
places here and giving it to the ones place. And to understand that
a little bit better, let me rewrite
these two numbers. Let me expand it out. So this 9 is in the hundreds
place, so it represents 900. The 7 is in the tens place,
so it represents 7 tens. And then, this 1 is in the ones
place, so it just represents 1. And then down here,
this 6 represents 600. This 5 represents 5 tens, or 50. And then, this
9-- well, it still just represents 9 ones, or 9. And we're subtracting this. We're subtracting
600 plus 50 plus 9. Or another way of thinking
about it, we're subtracting 600, we're subtracting 50,
we are subtracting 9. So let's work it out over here. So this is the
exact same problem, just written a little
bit differently. And we still have
the same issue. How do we subtract a larger
number from a smaller number? And the solution lies
in trying to take value from one of the other places. And the easiest place to go
is-- look, we've got 70 here. Why don't we take 10 from here,
and we'll be left with 60, and give that 10
to the ones place. So if you add 10 to
1, what do we have? Well, then we're
going to have 11. Notice, I have not changed
the value of the number. 971 is the same thing
as 900 plus 60 plus 11. It's still 971. And now we can
actually subtract. 11 minus 9 is 2. 60 minus 50 is 10. And 900 minus 600 is 300. So this subtraction should
result in 300 plus 10 plus 2, which is 312. Now, let's do the
exact same thing here, but we're going to do it
without expanding it out. So same issue-- how do
we subtract a 9 from a 1? Well, let's take a 10
from the tens place. We're going to regroup. So we're going to get
rid of one of these tens, so we're only going to have 6
tens left in the tens place. And we're going to give
that 10 to the ones place. So 10 plus 1 is 11. Now we are ready to subtract. 11 minus 9 is 2. 6 minus 5 is 1. 9 minus 6 is 3. We get-- let me do
that same color-- 312.