Get ready for 6th grade
Sal uses place value and a number line to subtract decimals, such as 1.5-0.7.
- [Instructor] What we're gonna do in this video is begin to practice subtracting decimals. And we're gonna build up slowly, and in future videos we're gonna 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. You could view this as 3/10, and then we're going to take away 2/10. If I have three of something and I take away two of them, well what am I gonna be left with? Well I'm going to be left with one, I'm going to be left with 1/10. And we can visualize this. Let me put a whole there, and this whole is divided into tenths, and 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. We want to take away, we're gonna take away 1/10, and then we take away 2/10. And so what are we left with? Well we're going to be left with this 1/10 right over here. That's the only tenth that is left of these 3/10. 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 one and 5/10, and from that we want to subtract 0.7, or 7/10. Pause the video and see if you can figure this out. 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 one plus 5/10, must 7/10, minus let me do it in that same blue color. Minus 7/10. And so there's a couple of ways that you could view it. You could view this as 10/10. One whole is 10/10, so this is 10/10 plus 5/10, minus 7/10. 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, one and 5/10 is the same thing as 15/10, minus 7/10. Minus 7/10. So 15 of something minus seven of it, well 15 minus seven is going to be eight. 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 it in one and 5/10, you could view this as if you could somehow put a 15 in the tenth's place, and instead call this zero 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've thought about it, let's go back to this step right over here, I could've said well look. I can think about what one minus 7/10 is going to be. I could view this as one minus 7/10, and then I'm going to add 5/10 to that. Then I'm going to add 5/10 to that. One minus 7/10, one is 10/10. If I take 7 of them away, I'm gonna be left with 3/10. So you could say that's going to be 3/10 plus 5/10. Plus 5/10. Which is once again, it is 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. Let's say this is zero, and then one, two, three, four, five, six, seven, eight, nine, 10. That is one. One, two, three, four, five. That is 1.5. We're gonna start at 1.5 right over here. That's 1.5. We're gonna take away 7/10. So one way that you might do it is you say okay, we could take away, we could take away 5/10, which would take us to one, and then we have to take two more tenths away, which is gonna 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 5/10. Minus 2/10. The reason why I broke it up like this is look, okay 1.5, or one 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 leftover to take away. One minus these 2/10, and once again, you are left with 8/10. These are all perfectly legitimate ways to tackle this problem. And this is a way that many people, including myself, would try to do it in their head.