The Associative Property of Multiplication 3 factor multiplication equations and parentheses

okay so today we are looking at something called the associative property the associative property so that is another mathematical property related to some of the other properties that we've already covered now in this case and again this this refers to multiplication in this case you have three factors okay remember factor is number and multiplication equation so in this case you might have something like two times three times five now that might look little bit weird right it's kind of hard to know where to start in problem like that now you can draw an array or you can draw out models you can use whatever you need to use to solve problem like this but the important part about the associative property is that it tells us this if you take and put parentheses around the first two factors right here and you make two times three times five you would do the the parenthesis first right so then you get the product of that two times three is six that would make this into six times five and then all you would have to know is that six times five is thirty which means that two times three times five is 30 okay so that's the first part however let's say you looked at this problem again you have 2 times 3 times 5 and you would rather do the 3 times 5 first well if you put parentheses parentheses around those that three times five and you decide to group those two factors instead you can still do that so you would have three times five is fifteen bring that two down then you'd have 2 times 15 which is 30. so if you can see right here we have it may look like two different equations but we actually have the exact same equations just grouped differently in this case we grouped the three times five and solved for three times five first in this case we grouped the two times three and solved for that first however we got the same product in every case so the associative property tells us that we can take three factor multiplication problems and we can break them up or group them differently depending on what works best for us in the situation so let's go ahead and let's try another one as an example here so let's go ahead and get rid of these and let's look at different one and this will work for any three factor multiplication problem and remember this is related to other ones in terms of things like the commutative property for instance which tells us that we can switch factors around as well right so the commutative property tells us that we have something like if we have something like 2 times 3 that's the same as 3 times 2 okay so in this case we're looking at something bit similar and similar to this the distributive property as well because we're able to group factors differently and still end up with the same product so let's look at another one let's say four times five times two okay so you have four times 5 times 2. let's go ahead and write that one out twice these are the exact same equation right you can see that they are the exact same equation now let's go ahead and break them apart little bit differently so this one we're going to take 4 times 5 first and this one we're going to do 5 times 2. now the rule is whenever you see an equation that already has parentheses always do the parentheses first okay it's going to make little note here equals first so in this case four times five well we know four times five you can get that in number of different ways you could break it apart the distributive factor excuse me the distributive property tells us that we can also break this into two times five plus two times five but that if that's easier or you can skip count by fives and many of you are very good at skip counting by fives in this case we know that the answer is 20 that's our product there now we're going to drop that two down and it's going to turn this into 20 times 2. well remember when you have twos you're always doubling the other factor right so really 20 plus 20 is the same thing as 20 times so you're going to end up with 40. okay now let's take look at this one 5 times 2 again you've got you have your twos and your fives these are some of the the easiest factors to work with and you all are very good at skip counting with both of these and remember again that with two as one of your factors you are doubling the other factor so 5 plus 5 is the same thing as 5 times 2. so in this case you're going to end up with 10 right you're going to drop that 4 down and now you've got 4 times 10 and remember our tens you will always have 0 in that ones place and with the identity property we know that four times one is going to be four so you end up with which means that in both cases no matter how we broke that up if we did 4 times 5 first or 5 times 2 you still get the same product okay so don't let these types of problems say in our math workbooks or anywhere else where you may encounter them don't let them fool you when you see these just because they're broken up differently does not mean that they are different equations they are the same equation okay and again like said you can also combine properties if you want to use the distributive property and break apart these numbers differently let's say we had much larger equation and you needed to break that apart you could certainly do that or equation with larger factors excuse me you could break that apart but just remember that even in this situation even if we did two times five plus two times five remember we're just doubling that five so now you know that together adding these together right equals 20 and then you do times two and you're still going to get 40. okay so that is very very quick primer on the associative property which refers to how you can break up three factor multiplication equations and we will continue working on these and go little bit further into it but you if you have questions please do let me know you