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### Course: 5th grade > Unit 3

Lesson 2: Subtracting decimals (tenths)# Strategies for subtracting more complex decimals with tenths

Learn all about subtraction of decimals, particularly those in the tenths place. The focus is on various strategies like decomposing whole numbers into tenths and using a number line for visualization.

## Want to join the conversation?

- If want you to subtract 3-1.5 don't you add two zero's to the 3 then add a decimal between 3 and the two zero's? Or is there another way to do it instead of doing that?(adding the two zero's and adding the decimal between the 3 and the zero's)(33 votes)
- Since .5 has only one digit, you only need to add a single zero, 3.0. Or break into parts, (3 - 1) - 1/2 = 2 - 1/2 = 1 1/2.(36 votes)

- why do we line up decimal points when adding and subtracting?(17 votes)
- We line up decimal points and stuff a lot because then we have a critically low chance of mixing up places, like thinking the tenths are in the hundredth, getting the whole thing wrong, and having to restart frustrated. Sorry no one answered you for a long time.(22 votes)

- Why did he say 1 and 0 tenths is 0 and 10 tenths?(9 votes)
- 1 and 0 tenths is the same as 0 and 10 tenths(11 votes)

- at4:52why does he add the 0.5?(7 votes)
- He broke 4.5 down into 4 + .5 and -2.8 into -2 - .8.(7 votes)

- I just made 2 into 2.0 and it was easier to solve it(9 votes)
- I know that division of decimals is not in this video, but just how do you divide decimals, say 0.58 divided by 0.12?(6 votes)
- Put it over the place value then do crisscrossed multication.(5 votes)

- Sal: Do some more examples subtracting decimals. So let's say we wanna figure out what two minus 1.2 is. Pause this video and see if you can calculate this. So there is multiple ways to tackle this. One way is you could say, "Look, this is the same thing "as two minus one "minus 2/10." This is two minus one and 2/10. So we're subtracting one, and we're subtracting 2/10. Now two minus one is pretty straightforward to compute. Two minus one is going to be one, and then we need to subtract 2/10 from that. So one is the same thing as 10/10. We could say this is 10/10. 10, write it this way. 10/10, and we're gonna subtract 2/10. What is that gonna give us? Well, that's going to give us, if we have 10/10, and we take away 2/10, that's going to give us 8/10. Lemme write it down here. 8/10, which is the same thing as 0.8, or 8/10. One way to think about this is if you're subtracting 0.2 from one, if you view this one as a 1.0, instead of expressing this as one, one, and 0/10, we are thinking about this as zero ones and 10/10. And when you think about it as zero ones and 10/10, well, 10/10 minus 2/10, it's easier to then think about, well, 10 of something minus two of something is gonna be eight of something. It's gonna be 8/10. Now we can also visualize this on a number line, so for example, let me draw a number line here, and so zero, one, two, three, four, five, six, seven, eight, nine. That's one, one, two, three, four, five, six, seven, eight, nine. That is two, so we're starting at two, and we're subtracting one and 2/10. So one way to think about it is we first subtracted one. We first subtracted one, and then we subtracted 2/10, and that got us to the point 8/10 on the number line. Another way to think about this, and the whole point here is to see multiple strategies and for you to think about what strategy you like the most and to realize they all get you to the same place. If you're thinking about it in a reasonable way, is you could use, what's the difference between two and 1.2? So 1.2 sits here on the number line, so what's the difference between two and one and 2/10? Another way to think about it is how many tenths do you have to add to one and 2/10 to get to two? Well, if you've already got 2/10, you need to add another 8/10 to get to the next whole. So you have to add 8/10, or you have to add 0.8. So the difference between two and 1.2, the difference between two and 1.2 is equal to 0.8.

Me: do 10 - 2 and and a period in front of your anwser and boom your done with the first question.(7 votes) - I feel tired. Don't you?(7 votes)
- OMG when I think about it yes! yes, I do .(1 vote)

- Another clear way to say 2 - 1.2 is putting down 20 - 12 which gives you 8.(7 votes)
- I'm confused about 4.5-2.8, wouldn't it be 2.3? why was the 1+1 added?(5 votes)
- No, the answer is 1.7. Sal was breaking down the problem into smaller and, arguably, easier steps.

1. Convert: 4.5 - 2.8 = 4.5 - (2.5 + 0.3)

2. Use the Distributive Property: 4.5 - (2.5 + 0.3) = 4.5 - 2.5 - 0.3

3. Use the Associative Property: 4.5 - 2.5 - 0.3 = (4.5 - 2.5) - 0.3

4. Subtract: 4.5 - 2.5 = 2

5. Replace the result of 4 in the converted equation: 2 - 0.3

6. Convert: 2 - 0.3 = (1 + 1) - 0.3

7. Use the Associative Property: (1 + 1) - 0.3 = 1 + (1 - 0.3)

8. Subtract: 1 - 0.3 = 0.7

9. Replace the result of 8 in the converted equation: 1 + 0.7

10. Add: 1 + 0.7 =**1.7**

As you can see, in step 6, the 2 was converted into 1 + 1. This is allowed because 1 + 1 is equal to 2.

Mathematical manipulations like this will become increasingly common the further you go into math. The idea is to make solving an equation easier, and you can change it however you want as long as those changes don't fundamentally change the result.

So, converting 2 - 0.3 into 1 + 1 - 0.2 is okay, but converting 2 - 0.3 into 2 - 0.3 + 0.3 would not be because it changes the answer.(1 vote)

## Video transcript

- [Instructor] Do some more examples subtracting decimals. So let's say we wanna figure out what two minus 1.2 is. Pause this video and see if you can calculate this. So there is multiple ways to tackle this. One way is you could say,
"Look, this is the same thing "as two minus one "minus 2/10." This is two minus one and 2/10. So we're subtracting one, and we're subtracting 2/10. Now two minus one is pretty
straightforward to compute. Two minus one is going to be one, and then we need to
subtract 2/10 from that. So one is the same thing as 10/10. We could say this is 10/10. 10, write it this way. 10/10, and we're gonna subtract 2/10. What is that gonna give us? Well, that's going to give us, if we have 10/10, and we take away 2/10, that's going to give us 8/10. Lemme write it down here. 8/10, which is the same thing as 0.8, or 8/10. One way to think about this is if you're subtracting 0.2 from one, if you view this one as a 1.0, instead of expressing this
as one, one, and 0/10, we are thinking about this as zero ones and 10/10. And when you think about it as zero ones and 10/10, well, 10/10 minus 2/10, it's easier to then think about, well, 10 of something minus two of something is gonna be eight of something. It's gonna be 8/10. Now we can also visualize
this on a number line, so for example, let me
draw a number line here, and so zero, one, two, three, four, five, six, seven, eight, nine. That's one, one, two,
three, four, five, six, seven, eight, nine. That is two, so we're starting at two, and we're subtracting one and 2/10. So one way to think about it is we first subtracted one. We first subtracted one, and then we subtracted 2/10, and that got us to the point
8/10 on the number line. Another way to think about this, and the whole point here is
to see multiple strategies and for you to think about
what strategy you like the most and to realize they all
get you to the same place. If you're thinking about
it in a reasonable way, is you could use, what's the difference between two and 1.2? So 1.2 sits here on the number line, so what's the difference between two and one and 2/10? Another way to think about it is how many tenths do you have to add to one and 2/10 to get to two? Well, if you've already got 2/10, you need to add another 8/10 to get to the next whole. So you have to add 8/10, or you have to add 0.8. So the difference between two and 1.2, the difference between two and 1.2 is equal to 0.8. Let's do a few more examples that get a little bit more involved. So let's say we wanna calculate what 3.8 minus 1.5 is. Pause the video and see
if you can calculate this. Well, just like before, we could view this as three minus one, so we're subtracting the ones plus 8/10 minus 5/10. Notice we have three and 8/10 minus one and 5/10, minus one and minus 5/10. And so now we can figure out, okay, three minus one, that's just going to be equal to two, and then 8/10 minus 5/10, well, that is 3/10, and so this is going to be two and 3/10, which of course we could write as 2.3. That seemed pretty straightforward. Let's do one that's a
little bit more involved. Let's say we wanna calculate
four and 5/10 or 4.5, minus two and 8/10 or 2.8. Pause the video and see
if you can calculate this. So you might wanna do
the exact same thing. You might say, "Okay, well,
this is the same thing. "Let's think about the ones." This is four minus two plus 5/10 minus 8/10. Four and 5/10 minus two and minus 8/10, minus two and 8/10. That's exactly what we have up here. Then you would say,
"Alright, four minus two, "that is two." But then you get to 5/10 minus 8/10, and there's multiple ways to tackle this, but you might say, "Oh,
how do I take away 8/10 "if I've only got 5/10 here?" And there's a bunch of strategies that you could think about. You could say, "Hey, what if I can get "some more tenths here?" So this is 5/10 minus 8/10. What if I could get some more tenths here? The best way I can think of it is like what if I were to break up these ones because one is 10/10? So I could view a two as one plus one, or I could view this as one plus 10/10. So if you view a two as one and 10/10, you can then just add those. You could then figure out what is 10/10 plus 5/10 minus 8/10? What is that going to be? Well, this is a little
bit more straightforward. 10/10 plus 5/10 is going to be 15/10, and if you have 15/10 and you take away eight of them, you're going to be left with 7/10. So this gets us to one plus 7/10, so all of this when you compute it, that is 7/10, which I could write as 0.7, which is equal to, so this is equal to one and 7/10. Now there's other strategies
that you could do here. One strategy that, and this is the one that I
typically do in my head is I write this as 4.5 minus 2.5 minus 0.3, or four and 5/10 minus two and 5/10 minus 3/10. Now why did I write it this way? Because I find this pretty
straightforward to compute, and then once I get that answer, I just have to take away 3/10. So for example, well, if I have 5/10 here, and I'm taking away 5/10, those are gonna knock each other out, and so I'm just gonna be
left with four minus two, which is gonna be two, and then I have to take away the 3/10. This is a pretty straightforward way of doing it in your head. So what's 3/10 less than two? Well, you can visualize a
number line in your head. Well, that's gonna be one and 7/10, one and 7/10, and if this feels strange how I got, oh, one, I wrote 7/100, one and 7/10. And if this seems strange
how I got there that fast, just think about this. This is the same thing as one plus one minus 3/10, and this one right over here is the same thing as 10/10, and so 10/10 minus 3/10. That over there is going to be, that is going to be 7/10, so it's going to be one and 7/10, which is what we got before. So the whole point here is to appreciate there's multiple strategies
for subtracting decimals, some that you can do a little
bit more automatically, but it's really good to think about what's going on in your head. And some strategies are
actually better in your head than on paper, or at least more easy in your head.