# Basic Properties of Gas

We’re going to take a look at some basic multiplication. So we just have five problems up here on the board that we’re going to work together to find the product of. Because that’s what the directions say: find the following products. So the product is what you get after you do the multiplication. It’s what goes after the equals sign. And so it’s important that you can just look at these numbers and be able to immediately tell what the product is going to be. Because for any multiplication that’s going on, as long as there’s no number higher than 12, you want to be able to just look at those numbers and be able to tell what the answer’s going to be because that’s going to save you a lot of time in future math problems. And so notice here throughout these five problems we never see a number higher than 12. So your goal should be to be able to eventually just look at all of these and know immediately what the product is going to be. But if you don’t, that’s fine because we’re going to go ahead and work through these problems. So we start out with 2 times 6. So this one’s pretty easy because we’re multiplying 2 times 6 and so this is basically 6 plus 6 because we have this number right here is telling us we have it’s the number we’re dealing with and then 2 right here is telling us how many of that number we have. So this is just 6 plus 6. But this is multiplication, so if it makes more sense to you, you can write it like this, so we could also look at it like this: 2 plus 2 plus 2 plus 2 plus 2 plus 2. I hope I’m confusing you; I’m just showing you some different says to approach this problem. So what we’re doing here is we’re just adding two 6s together so the answer is 12. Or we’re adding six 2s together, depending on how you want to look at it so 2 plus 2 is 4, plus 2 is 6, plus 2 is 8, plus 2 is 10, plus 2 is, again 12. Now when we come to this one, 5 times 3, here we know this has to be a multiple of 5. And so multiples of 5 always end up in 0 or 5. And so here, it’s really easy, because multiples of 5 are really easy to deal with in your head. So 5 plus 5 is 10, plus another 5 is 15. Now we’re going to go ahead and skip this one because this one may be the hardest one, so we’re going to come back to it. So now we have 4 times 11. And so whenever you are multiplying by 11, it’s really easy because you’re going to have the same digit twice. So if you do 2 times 11, the answer’s going to be 22. If you do 3 times 11, the answer’s 33. So 4 times 11, the answer’s going to be 44. So you’re just going to write this number twice. Now we come to 12 times 10. Now this seems like a really hard problem, and the easiest thing here may be just to work out this problem. 12 times 10, and work out the multiplication problem. So you get 120 that way. But an easier way to do it, is any time you’re multiplying something by 10, you can just take a 0 and add it to this number right here, so we just add a 0 to the end of 12 and get 120. Now this final problem is going to take a little bit longer to work out: it’s 7 times 9. So what we’re dealing here is we’re dealing with 9 plus 9 plus 9 plus 9 plus 9 plus 9 plus 9. We’re dealing with seven 9s all just added together. And so one way to approach it is, if you don’t know what 7 times 9 is, think about another multiple of 9. So maybe you know what 5 times 9 is, so you know that’s 45. So we multiply 5 times 9 and we get 45. But notice here that 5 is 2 less than 7, so we still need to add two 9s to 45. So here we can just add 9 plus 9. So 45 plus 9 is going to be 54, plus another 9 is, you guessed it, 63. So these are the products of these five multiplication problems. So again, you want, as long as there’s not a number higher than 12 in the multiplication problem you’re dealing with, your goal is to eventually just look at all of these and know immediately, 2 times 6, that’s 12. 7 times 9, that’s 63. 12 times 10, that’s 120. Because you’re going to need to know the answers to these multiplication problems many many times in life, probably on a daily basis, and so it’s very important to build this strong foundation in math. And so I hope my explanations helped you, and remember a couple of the tricks I taught you, especially with 4 times 11: any number times 11, you’re just doubling this number right here. So 4 times 11: 4-4, 44. 5 times 11, answer’s going to be 55. And then any time you’re multiplying by 10, just take the 0 from the 10, and put it at the end of this number, so that’s how we got 120.

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Last updated: 07/25/2017

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