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# Brug associativ lov til at forenkle multiplikation

## Video udskrift

in this video we're going to think about how we can use our knowledge of multiplying single-digit numbers to multiply things that might involve two digits so for example let's start with what is five times 18 and you can pause the video and see how you might try to approach this and then we'll do it together alright so if we're trying to tackle five times 18 one strategy could be to say hey can i reexpress 18 as the product of two numbers and the one that jumps out at me is that 18 is the same thing as two times nine and so I could rewrite five times 18 this is the same thing as five times instead of 18 I could write two times nine now why does this help us well instead of multiplying the two times 9 first to get the 18 and then multiplying that by five what we could do is we could multiply the 5 times the 2 first and you might be thinking wait wait wait hold on a second before you did the 2 times 9 first and now you're telling me that you're going to change the order that you're going to say hey let's multiply the 5 times 2 first is that ok and the simple answer is yes it is okay if you are multiplying a string of numbers you can do them in any order that you choose and so this is often known as the associative property of multiplication we can associate the two with the 9 first we can multiply those first or we can have an association with the 5 and the 2 we can multiply those two first now why is that helpful well what is 5 times 2 well that's pretty straightforward that's going to be equal to 10 so this is going to be equal to 10 let me do that same color 10 times 9 now 10 times 9 is a lot more straightforward for most of us than 5 times 18 10 times 9 is equal to 90 let's do another example let's say we want to figure out what 3 times 21 is pause this video and see if you can work through that there's multiple ways to do it but if you could do it the way we just approached this first example well as you could imagine we want to reexpress 21 as the product of smaller numbers so we could rewrite 21 as three times seven maybe and so if we rewrite it as three times seven and now we do the three times three first someone just put parentheses there which we can do because of the associative property of multiplication fancy word for something that is hopefully a little bit intuitive well then this is going to be equal to what's 3 times 3 it is 9 and then times 7 which you may already know is equal to 63 let's do another example this is kind of fun let's say we want to figure out what 14 times 5 is pause this video and see if you can figure that out well we could once again try to break up 14 into the product of smaller numbers 14 is two times seven so we can rewrite this as 2 times 7 or 7 times 2 and I'm running at a 7 times 2 because I want to associate the two at the 5 to get the 10 times 5 and then I could multiply the 2 times 5 first and so this is going to give us 7 times 10 7 times 10 which is of course equal to 70 one more example let's say we want to calculate 15 times 3 how would you tackle that well we can break up 15 into 5 times 3 5 times 3 and then we can multiply that of course by this 3 and then we can multiply the threes together first and then this amounts to 5 times 9 and 5 times 9 you might already be familiar with this this is going to be equal to 45 and another way to get to 45 you could say 5 times 10 is 50 so 5 times 9 is going to be 5 less than that which is also 45