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Strategies for subtracting more complex decimals with tenths

CCSS.Math:

Video transcript

some more examples subtracting decimals so let's say we want to figure out what 2 minus 1.2 is pause this video and see if you can calculate this so there's multiple ways to tackle this one way is you could say look this is the same thing as 2 minus 1 2 minus 1 minus 2 10 this is 2 minus 1 and 2 tenths so you were subtracting 1 and we're subtracting 2 tenths now 2 minus 1 is pretty straightforward to compute 2 minus 1 is going to be 1 and then we need to subtract two tenths from that so 1 is the same thing as 10 tenths we could say this is this is 10 10 10 right this way ten tenths and we're going to subtract two tenths what is that going to give us well that's going to give us with 10 tenths and we take away two tenths that's going to give us 8 tenths let me write it down here 8 tenths which is the same thing as 0.8 or eight tenths one way to think about this is if you're subtracting 0.2 from one if you view this if you view this one as a 1.0 instead of expressing this as 1 1 and 0 tenths we are thinking about this as 0 1 and 10 tenths and when you think about it is 0 ones and 10 tenths well 10 10 to minus 2 tens it's easier to then take oh and think about what kind of something - 2 of something it's going to be a - something's going to be 8 tenths now we can also visualize this on a number line so for example let me draw a number line here and so 0 1 2 3 4 5 6 7 8 9 that's 1 1 2 3 4 5 6 7 8 9 that is 2 so we're starting at 2 and we're subtracting 1 & 2 tenths so one way to think of is we first subtracted one we first subtracted 1 and then we subtracted 2/10 and that got us to the point 8 tenths 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 2 and 1 point 2 so 1 point 2 sits here on the number line so what's the difference between 2 & 1 & 2 tenths another way to think about it is how many tenths do you have to add to 1 & 2 tenths to get to 2 well if you've already got two tenths you need to add another 8 tenths to get to the next hole so you have to add 8 tenths or you have to add 0.8 so the difference between 2 & 1 point to the difference between 2 & 1 point 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 want to calculate what 3 point 8 minus 1.5 is pause the video and see if you can calculate this well just like before we could view this as 3 minus 1 so we're subtracting the ones plus 8 tenths minus 5 tenths minus minus 5 tenths minus 5 tenths notice we have three and eight tenths three and eight tenths minus one and five tenths minus 1 and minus five tenths and so now we can figure out ok 3 minus 1 that's just going to be equal to two and then eight tenths minus five tenths well that is three tenths and so this is going to be two and three tenths which of course we could write as 2 to point 3 that seems pretty straightforward let's do one that's a little bit more involved let's say you want to calculate 4 & 5 tenths or 4 point 5 minus two and eight tenths or 2.8 pause the video and see if you can calculate this so you might want to do the exact same thing you might say okay well this is the same thing let's talk about the ones this is four minus two plus five tenths plus five tenths minus eight tenths minus 1/10 four and five tenths four and five tenths minus two and minus 8 tenths minus two and 8/10 that's exactly what we have up here and you would say all right 4 minus 2 that is 2 but then you get to five tenths minus eight tenths and there's multiple ways to tackle this but you might say well how do I take away eight tenths if I've only got five tenths here and there's a bunch of strategies that you could think about you could say hey what if I can get some more tense here so this is five tenths five tens minus eight eight tenths what if I could get some more tense here the best way I could think of it is like what if I were to break up these ones because one is ten tenths so I could view a two I could view a 2 as 1 plus one or I could view this as 1 plus 10 10 10 10 so if your view a 2 is 1 and 10 tenths you can then just add those you could then figure out what is 10 tenths plus 5 tenths plus 5 tenths minus 8 tenths minus 8 minus 8 tenths what is that going to be well this is a little bit more straightforward ten tenths plus five tenths is going to be 15 tenths and if you have 15 1010 you take away eight of them you're going to be left with seven tenths so this gets us to one plus seven tenths so all of this when you compute it that is seven tenths which I could write as 0.7 which is equal to so this is equal to 1 1 and 1 and 7/10 now there's other strategies that you could do here one strategy that this is the one that I typically do in my head is I write this as 4 point 5 minus 2 point 5 minus 2 point 5 minus 0 point 2 3 or 4 and 5/10 minus 2 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 going to knock each other out and sewed I'm just going to be left with 4 minus 2 which is going to be 2 and then I have to take away the 3/10 then I have to take away the 3/10 so this is a pretty straightforward way of doing it in your head so what's 3 tenths less than 2 well you can visualize a number line in your head well that's going to be 1 and 7/10 1 and 7/10 and if this feels strange how I got a 107 hundreds 1 and 7/10 and that this seems strange how I got there that fast just think about this this is the same thing as 1 plus 1 minus 3/10 and this one right over here is the same thing as 10 tenths and so 10 tenths minus 3/10 that over there is going to be that is going to be 7/10 so it's going to be 1 & 7 tenths 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