More advanced subtraction strategies with hundredths

So let's say we wanted to compute 8 and 38 hundredths minus 4 and 54 hundredths. See if you can pause this video and figure it out on your own.

There are multiple strategies for doing this. I'll tell you the way that my head likes to do this. I would view this as the same thing as 8 and 3800s and then I would subtract 4 and 38 hundredths. The reason why I pick 3800s is that will cancel out. It'll take away these 3800s, and then I still have to subtract a little bit more. If I already subtract 38 hundredths, well, I have to subtract a total of 54 hundredths.

So let's see, 54 is how much more than 38? And I am doing this in my head as I speak. Let's see, to go from 38 to 48, I need six, and I need 10 more, so I need to subtract another 16. I need to subtract another 16 hundredths. And how did I think about that? Well, 54 is 38 and 16. So if I'm subtracting 54, I could break that up.

I could subtract 3800s, and then I could subtract 1600s. Why did I pick 3800s? Because it matches up with this. If I say 8 minus 4 is going to be 4, and then I have 38 hundredths minus 38 hundredths. Well, those are just going to cancel out with each other. So this minus that is just going to be four, and then I'd say 4 minus 16 hundredths.

So how do we think about that? Well, you might be able to do this in your head at this point. You might say, "Okay, well, I have to go 16 hundredths less than four." That's going to be three and 84 hundredths. Or you might want to just break it up. You could say, "Okay, four is the same thing as 3 + 1 + 100 hundredths," and then I want to take away minus 16 hundredths.

Well, 100 - 16 is 84, so this is going to be… this part right over here is 84 hundredths. I'll write it out as hundredths, which I can write as 0.84. And 3 + 0.84, well, that's going to be… this is going to be equal to, and we figured out already multiple times, 3 and 84 hundredths.

Now, as I said, there are multiple ways that we can try to tackle this. For example, another way that I could do this one right over here is I could say, "All right, let me… let me do the ones." So I'd say 8 minus 4.

8 - 4 plus… let me try to do the tenths. So I could have 310 - 510, 0.3 - 0.5, and then I would have the hundredths. So 800s minus 400s. So plus 800s minus 400s. Now, this is pretty easy to compute. This is pretty easy to compute.

But what about this? I don't have 510 to take away. Well, what I could do is instead of having an eight here, I could take one away from it and make that a seven. So I have one that I can regroup someplace over here. I can reorganize it.

So I could do this: a 7 + 1010. And so I can take those 1010. I could take those 10/10 and add them right over here. So let me rewrite this. I could rewrite this as 7 - 4 + 1010 plus 310. And I'm actually… let me just write it all as plus 310. I'm mixing different ways of writing it this way, but that might be good.

Minus 510. And then this part I could just compute. This is plus 400s, plus… let me do that color… plus 400s. This right here is going to be 400s. Now what is this going to be? 7 minus 4 is going to be 3. 10/10 + 310.

Let me use the right color. So this is going to be three, and then 10/10 + 3/10 is 13/10 minus 5/10 is 8/10. And then I have 4 hundredths. So once again, 3.84, 3 ones, 8/10, 400s, or 3 and 84 hundredths.