Distributive Property of Multiplication 3 rd Grade Math Made Easy

foreign so welcome to today's lesson on the distributive property of multiplication now the word distribute simply means to divide into shares want you to take look at this group of people they're working at food distribution center and they're giving out food into shares this is how they're Distributing their food the distributive property of multiplication is sometimes called the break apart strategy take large amount and you break it apart like this array this array has total of one two three four rows with one two three four five columns or five in each row would break it apart and then what I'm doing is pretending this part does not exist we're going to focus on just this part of the array which is the factors for this part of the array are four and three so the multiplication number sentence for this part is four times three equals twelve now let's pretend that I'm taking the same array and I'm moving my Square okay now focus on this part of the array this part of the array has one two three four any four rows and two in each row by factors of four and two the multiplication number sentence for this part of the array is four times two equal can't keep that in mind so whether break what no matter how break apart my array on this part the left side it's 4 times 3 equals twelve and the equation for the other sign is four times two equals eight so now take those two multiplication number sentence and add them together add my answers together my answer is 12 and my answer of eight so 12 plus 8 equals twenty and that's my final answer twenty one more time so this array has one two three four rows with one two three four five in each row so since four times three is twelve and four times two is eight twelve plus eight is twenty so four times five is twenty so let's use some Thanksgiving types of arrays to show our understanding here see one row two three four five rows also see one two three four five six seven in each row now know I'm working with factor of seven and factor of five five times seven but I'm going to use the break apart strategy or the distributive property to show my understanding so I'm gonna break it apart into an easier number that can work with let's say break it apart this way and your lines don't have to be perfectly straight it's perfectly fine but most importantly let's focus on the array on this side okay so here have still one two three four five rows and the amount in each row is two so two is my second Factor on this side of the equation five times two equals ten so focusing on the right side of the array now have one two three four five total columns remember still have one two three four five rows so this side of the array is now factors five and five so that's five times five equals 25. if you count every single one of these turkeys in this part of the array on the right side you will get total of 25. so let's take those two answers that just got 10 from this number this multiplication equation remember this is the left side of the array that broke apart and then 25 from the right side of the equation that's 10 plus 25. five plus zero that's five two plus one that's three so that's 35. so now take that all the way back to my original factors that started with five times seven equals thirty five also want you to notice something else let's erase it all now you can choose to break apart the array in either with horizontal lines going this way or vertical lines going this way it doesn't matter how you break it apart it the most important thing is that you get the answer correct now when we consider let's say we consider the amount in each row one two three four five six seven right now when if break it apart no matter how break it apart let's say break it apart this way what we're essentially doing is taking the number seven and we're breaking it apart into three plus four do you see that on this side there's three and on this side there's total of four know it starts with four five six seven right here but it's really one two three four so three plus four is seven that's how I'm breaking it apart so when take when consider the three here I'm really doing one two three four five rolls five times three broke apart the seven so it's essentially five times three plus five times four the four the five Remains the Same for the amount of rows on this side of the array but now my the amount in each is four so that's where my four and my three come from but when add those together three plus four that would give me an answer of seven Okay so sometimes you might see the break apart strategy or the distributive property written like this five times three plus four right and what that really means is that you're gonna multiply whatever is inside the parentheses remember these are called parentheses you're going to multiply whatever is inside the parentheses by five so it will be five times three and then plus five times four okay so the answer you get for five times three which is fifteen and the answer you get for five times four which is twenty if add those together do get the same answer as five times seven considering that three plus four is seven let's see fifteen is my answer for five times three twenty is my answer for four times five times four four times five add those together and it's like math magic you do get 35. so in the break apart strategy can be looked at in two or more different ways it can be looked at breaking apart the array into two numbers that make that when you add them together you still get the same number like three and four can you think of some other ways that can break apart for seven the number seven think about some ways that can break apart the number seven did you say two and five we did that earlier very good what if tried six and one would that work absolutely it would work all right let's try to erase all of that and continue on to the next one so remember or can look at it different way can can also say breaking apart the number five breaking apart the number five can break it apart to two plus three or could break apart the number five two four plus one or one plus four that means would have to break it let's let me erase and show you that means would have to bring let's say break it apart too five break the five apart into two plus three that would be one two and one two three so instead of having five I'm having three on this side two on this side but look at this the one two three four five six seven in each row Remains the Same so we're looking at this sign to be two times seven and this side would be three times seven wonder if would still get the same answer well two times seven is fourteen three times seven is twenty one let's see I'm you remember the answer I'm supposed to get remember it's 35 good job so let's add fourteen plus 21 4 plus 1 that's five two plus one that's three like it's mathematic 35 again every time no matter how break apart my array will still get 35. so let's go ahead and go through the other problems this is corn sometimes during Thanksgiving we enjoy good corn on the calm you help you figure out how you might want to break this apart let's first count the total in each row well got the total amount of rows of corn we see first there's one two three rows there's one two three four five six seven eight nine nine in each row or nine columns so know that my factors are nine and three so it's three times nine is what I'm looking for but let's break it apart nine is odd number so can't break it apart evenly so maybe if just go with four or can go with two again no matter what how you break it apart it will be totally fine let's go with let's break it apart right here so hope you notice by now that now that break it apart this way this side of the array has three in each row and four this time in each row so that's four times I'm sorry three rows and four in each row right three times four equals you guessed it twelve okay now let's look on the right side of the array here we have and let's just erase just to make sure that it's not too confusing because we counted the original part of the array here we go with counting we still have one two three rows that didn't change because we didn't break apart the rows we broke apart the columns so we still have three rows but now we have one two three four five total of five in each row my factors are three and five so in this part of the array my multiplication number sentence is three times five three times five is equal to Fifteen let's add up the answers we get so that's twelve plus fifteen and that should give me the answer for three times nine five plus two that's seven two one plus one that's two twenty-seven so three times nine equals twenty seven now take it another step notice the let's change color little bit notice that the four and the five so like this is the four and the five factors when do add those two together four plus five that also gives me the total that is right here which is nine 4 plus 5 equals nine so in all in actuality I'm still working on breaking apart the nine into four plus five all right hope that makes sense let's move on to our next array now this array would be something that you would see in Thanksgiving maybe you're covering your food but this is huge array let's go ahead and count the amount of rows that we see in the amount of columns as well so we have one two three four five six rows one two three four five six seven eight eight columns or eight in each row so my factors are six and eight so my multiplication sentence is six times eight and if don't know that answer what I'm gonna do is split apart my array into numbers that can work with easy so have the choice can split my array in using horizontal line where split it in half this going this way or maybe would choose to use vertical line instead and my vertical line would go this way would choose to split it in half either way that way whatever is on one side of my array would be the same answer in the other side so your choice doesn't matter either way your ends will still be the same so let's try splitting it this way which means I'm splitting the eight into four plus four okay within parentheses and then six times four plus six times four notice my Factor here is six so this part of the array is six times the left part of the array is six times four the right part of the array is also six times four why even though know have the five six seven eight here we really are working with one two three four four in each row or four columns and one two three four five six rows so on both sides of the equation we're working with six times four and on this side of the equation we're also working with six times four do you know the answer for six times four well that is twenty-four six times four plus six times four is twenty four plus twenty four and the answer to that is 48 so take this all the way back to my original factors six times eight is forty eight and it's like bath magic once again let's go ahead and erase all of this and what I'm going to show you erase what I'm going to show you is that even if choose to split maybe some of you choose to split your this particular array into using horizontal line instead of vertical line and if we use the horizontal line instead of vertical line would graphic cut it this way that way on one side of my equation will be equal to the other side of well not my equation but my array would be equal on both sides so here have one two three rows in the top part of my array and have one two three four five six seven eight so I'm my multiplication number sentence because my factors are three and eight is three times eight on this side of the array three times eight is twenty four once again and then one two three really didn't have to do this all over again because can clearly see that both sides are exactly the same so there we go again eight as my fat one of my factors and three is my other factor and so my multiplication sentence down here would be three times eight equals twenty four again we're adding 24 plus 24 still getting the same answer as 48 can't escape it same answer so 6 times 8 is 48. let's try one more here we have Delicious Pies hopefully during Thanksgiving you would get chance to eat Delicious Pie let's count the rose one two three four rows how many are in each row well that's one two three four five six seven in each row perfect so now my factors are four and seven so that's four times seven don't know what the answer is quite yet but I'm gonna take this opportunity to split my array apart into halves foreign apart like so okay now that split my array apart what is what are my factors on each side well on this side my factor is 2 times 7 which is 14. also on this side of my array my factors are two times seven which is also 14. that makes it easy to add so 14 plus 14 for plus four that's two that's eight two one plus one that's two that's total of 28. going back to my original Factor seven four times seven or seven times four my answer or my product is twenty-eight there you have it my friend that's the break apart strategy remember we can choose two if we have large number to work with we can choose to break it apart or break this apart could have broken this apart by three plus four or in this case chose to break apart the four instead so the four was two plus two so was working with two plus two times seven so that's seven times two plus seven times two the answer you get for each is fourteen plus fourteen that answer is Twenty Eight hope that makes sense my friends and if you have any other questions any other concerns be sure to try my worksheet that will be attached to this for extra practice thank you for joining me on this video have wonderful day bye bye foreign foreign foreign foreign foreign