Strategies for subtracting basic decimals

Going to do in this video is begin to practice subtracting decimals, and we're going to build up slowly. In future videos, we're going to learn to do this faster and faster, and doing it for more and more complex situations.

So let's say we have 3/10 minus 2/10. What is this going to be? Well, there's a bunch of ways you could tackle it, and I encourage you to pause the video and try to do it on your own before I work through it with you. But I'm assuming you did that, so let's do it together.

So you could view this as 3/10, and then we're going to take away 2/10. So if I have three of something and I take away two of them, what am I going to be left with? Well, I'm going to be left with one. I'm going to be left with 1/10th.

We can visualize this. Let me put a hole there, and this hole is divided into tenths. We see that three of the tenths are already highlighted. So these three green bars you can visualize as 3/10. Now we want to take away 2/10.

So we're going to take away one tenth, and then we take away 2/10, and so what are we left with? Well, we're going to be left with this one tenth right over here. That's the only tenth that is left of these three tenths.

So now let's build on that idea and try to tackle more complex situations. Let me delete this and this and let's say we want to tackle 1.5, or 1 and 5/10. From that, we want to subtract 0.7, or 7/10. Pause the video and see if you can figure this out.

So there's a couple of ways you could think about this, and I'll tell you the way that I do it in my head. You could view this as, so let me rewrite this: you could view this as 1 plus 5/10 minus 7/10.

So there's a couple of ways that you could view it. You could say this is 10/10. One whole is 10/10, so this is 10/10 plus 5/10 minus 7/10. And so you could say this is 15/10. If you're doing it in your head, you might get to this faster. You might say, "Hey, 1.5, 1 and 5/10 is the same thing as 15/10 minus 7/10."

So 15 of something minus 7 of it, well, 15 minus 7 is going to be 8. So this is going to be equal to 8/10. The way I just did it, I just thought of everything in terms of tenths. Instead of thinking of 1 and 5/10, you could view this as if you could somehow put a 15 in the tenths place and instead call this 0 ones and 15/10, and then you subtract 7/10 from those 15/10 to get the 8/10, which would be 0.8 or 8/10.

Now another way that you could have thought about it, let's go back to this step right over here. I could have said, "Well, look, I can think about what 1 minus 7/10 is going to be." So I could use 1 minus 7/10, and then I'm going to add 5/10 to that. So then I'm going to add 5/10 to that.

So 1 minus 7/10. 1 is 10/10, so if I take seven of them away, I'm going to be left with 3/10. So you can say that's going to be 3/10 plus 5/10, which is once again equal to 8/10.

Now another way that you could tackle this, and once again, I'm showing as many ways as possible just so you appreciate that these are just different ways of tackling the same idea. Let's draw a number line here.

So let's say this is zero, and then one, two, three, four, five, six, seven, eight, nine, ten. That is one, one, two, three, four, five. That is 1.5. So we're going to start at 1.5 right over here.

So that's 1.5, and we're going to take away 7/10. So one way that you might do it is you say, "Okay, we could take away five tenths," which takes us to one, and then we have to take two more tenths away, which is going to take us to 8/10 or 0.8.

So the way that I just thought about it just now is I said, "Hey, this is the same thing as 1.5 minus 5/10 minus 2/10." The reason why I broke it up like this is like, "Okay, 1.5 or 1 and 5/10 minus 5/10, that's pretty straightforward to compute." You could say that right over there is just going to be one.

I'm taking away the 5/10, and then I have 2/10 left over to take away. So one minus these two tenths, and once again, you are left with 8/10.

So these are all perfectly legitimate ways to tackle this problem, and this is the way that many people, including myself, would try to do it in their head.