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

Video transcript

So let's subtract 286 from 913. But first I'm going to do it
in a slightly different way. I've taken each
of these numbers, and I've expanded them out. This 9 in the hundreds
place represents 900. This 1 in the tens
place represents 10. This 3 in the ones
place represents 3. Likewise, 286 is the same
thing as 200 plus 80 plus 6. So let's try to subtract
going place by place. So if we start in
the ones place, we have a problem immediately. 3 is less than 6. How do we subtract a larger
number from a smaller number? We also have a problem
in the tens place, 80 is larger than 10. How do we subtract a larger
number from a smaller number? And you might guess the answer
here is regrouping, sometimes called borrowing. We're going to take
value from one place and give it to another. So let's say this
scenario right over here, where we have this
3, and we want to take some value from
one of the other places. Well, I could take 10
from the tens place, so then this is
going to become 0. And if I give that 10 to the
ones place, so 10 plus 3 is 13. Notice I haven't
changed the value. 900 plus 0 plus 13 is still 913. Now, this solved the
problem for the ones place. I can now subtract 6 from 13. But it made the problem in
the tens place even worse. I now have to
subtract 80 from 0. What do I do? Well, luckily, I can go
to the hundreds place. I could take 100 from 900,
so then I'm left with 800. And I could you give
it to the tens place. So if I give it to
the tens place, then this is going to be 100. Notice this still
adds up to 913. 800 plus 100 plus 13 is 913. Why is this valuable? Well, now in every column, I'm
subtracting a smaller number from a larger. You might say, wait, isn't
there a positive sign here? But we have this
negative out here. So we're subtracting 6 from 13. We're subtracting 80 from
100, subtracting 200 from 800. So let's do it. 13 minus 6 is 7. 100 minus 80 is 20. 800 minus 200 is 600. So we're left with 600 plus
20 plus 7, which is 627. Now let's do the
exact same thing here, but we're not going to
expand out the numbers. So 6 is greater than
3, what do we do? Well, we can regroup
from the tens place. We can take 10 from here
so we're left with 0 tens and give that 1 ten
to the ones place. So you give 10 to
the 3, it becomes 13. But now we have a problem
in the tens place. How do we subtract 8 from 0? Well, we could take 100
from the hundreds place, so 900 becomes 800, and give
that 100 to the tens place. So you give the 100 to the tens
place, 100 plus 0 tens is 100. 100 is the same
thing as 10 tens. And so now we are
ready to subtract. 13 minus 6 is 7,
10 minus 8 is 2. Remember, this is really 10
tens minus 8 tens to get 2 tens. 100 minus 80 to get 20. And then finally, we have 800
minus 200 to get 600-- 627.