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CCSS.Math:

I want to think about
all of the different ways we can represent value
in the number 21.3. So one is to just look straight
up at the place values. This 2 is in the tens place, so
it literally represents 2 tens. So this is equal
to 20, 2 times 10. This 1 is literally equal to 1. It's 1 one. And then this 3 is
3/10, so plus 3/10. But now I want to
rearrange or regroup the value in these places. So, for example, I could
take 1 from the ones place and give it to the tenths place. So let's see how
that would work. So we're going to take 1
away from the ones place, and so it's going to become a 0. And we're going to give
it to the tenths place. And what we're going
to see is that that's going to make the
tenths place into 13/10. Now, does that actually make
sense that I took 1 from here and it essentially added
10 to the tenths place? Well, let's rewrite
what this represents. So we still have 2 tens. So this is still
going to be 2 tens. Now we have plus 0 ones. And we essentially wanted to
write that 1 that we took away from the ones place
in terms of tenths. So if we were to write
this in terms of tenths, it would be 10/10 plus the
3/10 that were already there. And so this is going
to be equal to 13/10. Let me write that down. So this is equal to 20. That's the color you can't see. This is equal to 20 plus 0
ones, so 2 tens plus 0 ones plus 13 tens. Let's do another example
with this exact same number. So once again, 21.3. And I'll write it out again. This is equal to 20 plus 1. We'll do that in
the purple color. Plus 1 plus 3/10,
plus 3 over 10. Now, I could take 1
from the tens place so that this becomes just 1. Now what do I do with that 10? Well, let's say with that 10 I
give 9 of it to the ones place. So I give 9 of it to the ones
place so that this becomes 10. And I still have 1 left
over, and I give it to the tenths place, so
that's going to become 13/10. So what did I just do? Well, I could rewrite this. Let me be clear what I did. This is the same
thing as 1 plus 9. Actually, let me
write it this way. 1 plus 9 plus 1. That's obviously
the same thing-- 10 plus 9 plus 1 is the
same thing as 20. And of course, we have what
we have in our ones place, plus 1 plus 3/10. And what I want to do is I want
to take this 9, the 9 that I took from the tens place
and give to the ones place. And I'm going to take this 1
that I took from the tens place and give it to the tenths place. So 1 is the same thing as 10/10. And so when you
regroup this value, you get this as being equal
to 10 plus-- 9 plus 1 is 10, and then 10/10
plus 3/10 is 13/10. So that's all that
happened here. I changed the value
in the places. I took 1 ten away. I had 2 tens. Now I'm only left with 1 ten. And that extra 10 of
value, I regrouped it. I gave 9 to the ones place. So 1 plus 9 is 10. And then I gave 1
to the tenths place. So 1 plus 3/10 is the
same thing as 13/10.