Main content

## Get ready for 4th grade

### Course: Get ready for 4th grade > Unit 3

Lesson 7: Distributive property# Distributive property when multiplying

CCSS.Math:

Sal uses the distributive property to break up 4x7 into smaller numbers.

## Want to join the conversation?

- why did he meow and why did he say yup there still mad(24 votes)
- because he's trying to act funny, it is pretty funny. - _ -(8 votes)

- what is 7 times 7(23 votes)
- The answer is 49(3 votes)

- can you use angry cats more often?(15 votes)
- i don't understand Distributive property.(6 votes)
- i think the problem is that they dont teach people a definition, i am a bit late to answer but heres my try.

if i am incorrect anywhere, please flag this answer as i am rarely active and comment where did i go wrong so other people do not make the same mistake, thank you so much 8)

Firstly, this is my definition.

Distributive property lets us distribute any value of mathematics into a combination of operations. It is helpful in creating or solving problems. All questions are just either simple or complex distributions of the final answer. You just have to find out how the value got distributed into the question and what that real value is.

then the weird long story explanation.

so every mathematical number or group of numbers, they all can be obtained by more than one possible ways, for example, you can get 3 by so so so so many ways, think of some ways you can get the number 3 in maths. let me start. if you take away 24 candies out of 27 candies from your sisters candy jar, she will have 3 candies left. so 27 - 24 = 3. Now think of some more of the other ways you can get a 3.

like 6-3 or 5+20+13+2-37.

Now here is the most amazing part. when you see a three anywhere in school or at home, you could 'DISTRIBUTE' that 3 in so many different ways too, you could literally write the long operations or terms we used above to express a 3, like 100-97 or 1+2 or 1+1+1. SO intead of that one simple three, you can write all the different ways in which you could distribute the value of 3. The number 3 is nothing but a value, do not focus too much on the symbol.

This 7-4 could also be written in place of 3 anywhere in the world, 3 is just a value, a reality. A value in my opinion is a reality that we see, acknowledge and try to communicate it to the people around us. So we assign a symbol to it for easier communication. 3 isnt just this symbol, neither is any other maths value. It could be anything, three could be this iii or this hhh or yyy or brickbrickbrick or ballballball.

But when it comes to multiple mathematical operations, like 3 + 7 x 5. In this maths operation, you can still substitute the value of three with lets say 80-77, but now in this case of " 3 '+' 7 x 5 " you will have to put this 'DISTRIBUTED VALUE OF 3' in brackets or parenthesis. Because otherwise you might end up 'commutating' (means moving around) the multiplication to one of these 'DISTRIBUTIONS of 3' and get to the wrong answer. That is why the order of operations exists, or the order of solutions exists where we always solve the parenthesis first, because that way we could identify what is the real value of whatever is inside that parenthesis and then we could just use that real value and add/subtract/multiply/divide it with other real values to finally get to our real answer.

in simple terms lets say we distributed 3 into 5+6-40+26,

now lets put this into our example above of 3 + 7 x 5.

if we just use 5 + 6 - 40 + 26 + 7 x 5, we wouldnt know which numbers are the combined distribution of the real value, obviously here we know which are because we have already specified that for the sake of understanding. if we solve it as is we get 32, if my calculations are right haha. But in reality thats not the answer. if we solve 3 + 7 x 10 we would get 38. SO we have to specify it in brackets/parenthesis which are the terms that we distributed 3 into. like (5 + 6 - 40 + 26) + 7 x 5. Here we first solve the parenthesis as per the rules**which exist so that we dont stray away from the real answer**and then get the answer 38.

everything in maths, it might look all big and scary but it already has an answer. An answer from which it was distributed into this long scary thing. the same thing goes for almost every mathematical equation or operation in higher classes too. They are all just one term blown up into this big complex terms. just focus on finding the real value of it all.

Pay attention to the wording here. most of science and maths is just very easy if you learn and know the literal meanings of the names of things and focus on that. Because most namers try to put everything that is in the explanation of that thing, into one or two words which could tell any reader the general sense of what is in that topic.(9 votes)

- Give this a ton of votes.(10 votes)
- hi can you help me with multipacaitoion(9 votes)
- i need help on a question its 8 x 4 but the first problem you did(7 votes)
- I believe you have the answer already, and this is a year later, but I would just like to say that 8 and 4 are both even numbers. Which, if you watched the video, means that you are able to sperate them evenly. For instance, 4, can be separated by 2. 8 may be separated by 4.(3 votes)

- I don't understand the distributive property.(6 votes)
- you just break the array in half and then do that multiplication(2 votes)

- I got the achivement of seingthis video for an hour omggg :D(7 votes)
- What is the easiest way to learn my 7 times table? This is very hard.(0 votes)
- Many kids have difficulty with 7’s, but this does not have to be you if you use a strategy.

There are multiple strategies. Here are three of them. These strategies come from the idea that multiplication is the same as counting groups of objects (distributive property).

1) If you’re good with 2’s and 5’s, a possible way to multiply a number by 7 is to multiply it by 2, multiply it by 5, then add the results. This is based on the fact that 2 + 5 = 7.

Example: let’s do 8 x 7.

8 x 2 = 16

8 x 5 = 40

16 + 40 =**56**, the answer.

2) If you’re good with 10’s and 3’s, a possible way to multiply a number by 7 is to multiply it by 10, multiply it by 3, then subtract the results. This is based on the fact that 10 - 3 = 7.

Example: let’s do 8 x 7 again.

8 x 10 = 80

8 x 3 = 24

80 - 24 =**56**, the answer.

3) lf you’re good with 6’s, a possible way to multiply a number by 7 is to multiply it by 6 and add the original number. This is based on the fact that 6 + 1 = 7.

Example: let’s do 8 x 7 again.

8 x 6 = 48

original number = 8

48 + 8 =**56**, the answer.

These are not the only strategies. From looking at the ideas in the three strategies l wrote, you might even come up with your own strategy that you like better.

Have a blessed, wonderful day!(17 votes)

## Video transcript

- [Instructor] What we're
going to do in this video is dig a little bit deeper into our understanding of multiplication. And just as an example, we're going to use four times seven. And some of you might know
what four times seven is, but even in this case, I think you might get
something from this video because we're gonna think
about how you can break down a multiplication question
into simpler parts, and that's going to be useful
well beyond four times seven. It's going to be useful in your future when you're tackling more
and more complicated things. Now there's a couple of
ways that we can visualize four times seven. My favorite way is to
visualize it with angry cats, so let's bring on the angry cats. (imitates cats meowing) Yep, they're still angry. And we can see that
this is a representation of four times seven. We have four rows right over here. Four rows, and each of those rows have seven cats. And so you can see that right over here, each of those rows has seven cats. Some people would call
this a four by seven grid or four by seven array, however you want to view it, but if someone were to ask
you what's the total number of cats, it would be four
rows times seven columns, four times seven. Now another way to
represent four times seven is also with a tape diagram. You might see something like this, where here, we're visualizing
it as seven fours, or you could view it as
four plus four plus four plus four plus four plus four plus four. Now that's all well and good
and you can add that up, if you like, but what I promised you is
that we would figure out ways to break down things that might simplify things in the future. Well what if you didn't know
what four times seven is, but you knew what four times five is and you knew what four times two is? Well what's interesting is
that seven is five plus two, so what if we tried to first
figure out this many cats, so four rows and five
columns right over there, and then we tried to figure out this many cats? Four rows and two columns. And you can see that it's the
exact same number of cats. So one way to think about
it is four times seven is the exact same thing as four times, and I'm gonna use parentheses,
and that just means to do that part first,
is equal to four times, instead of seven, I could write that as five plus two, 'cause that's what seven is, so all this is saying is four time seven is the same thing as
four times five plus two, where you do the five plus two first, 'cause we have those
parentheses around it, and five plus two is,
indeed, equal to seven, and we can see that that is
equivalent to the total number of cats that we have here, which we could view as
what we just circled off in this orangeish pink color which would be four rows of five, so that would be equal to four times five. Four times five, and then to that, we can add
this second group of cat heads or angry cat heads, and that is four rows of two. So that's four times two, and we could put parentheses if we want, just to make it a little
bit more readable. Now why did I do that? Well, some folks might
find four times five a little bit more straightforward. I could skip count by five. I can go five, 10, 15, 20. Also four times two might be a little bit more straightforward, and so it could be easier to say hey, this is just going to be four times five, which is 20, plus four times
two, which is equal to eight, and so that is just
going to be equal to 28. And you could have thought
about it the same way down here with what is sometimes
called a tape diagram. We could say, all right, if I have five fours, that's this mount right over here. That is the four times the five, and then I could add
that to the two fours, the four times the two right over here, and that's another way to
get to four times seven. So the big picture here is
even if you're not dealing with four times seven,
if you're not dealing with angry cats, and in most of our lives, we actually try to avoid angry cats, there might be a way to
break down the numbers that you're multiplying into ones that you might be more familiar with. I'll give you one more example. Let's say someone were to ask you, well, what is six times nine? Pause this video and see
if you can break this down in some useful way. Well, maybe you know what six times 10 is, and you also know what six times one is, so you could rerwrite nine as 10 minus one. Well then this would
mean that six times nine is the same thing as
six times 10 minus one. Based on exactly what we just did up here, that says that this whole thing is going to be the same
thing as six times 10. Six times 10 minus six times one. One way to think about it is, I just distributed the six. That's the distributive
property right over there, and then six times 10 is equal to 60, and then six times one is equal to six. And it might be easier for me to say, hey, 16 minus six in my head, that's equal to 54. So I know what some of you are thinking. Six times nine seems so clean, and now I've involved all
of this other symbolism, symbols, and I've written
down more numbers, but at the end of the day, I'm trying to give you skills for breaking down problems and including ways that you might want to do it in your head. If you're like, hey, I'm kind of foggy on what six times nine is, but six times 10, hey, I know that's 60, and six times one, of course, that's six, well what if I view this
as six times 10 minus one? And then I could tackle it and get 54. And once again, you might know six times nine. You might know four times seven, but in the future, it might be useful for
bigger and bigger numbers to think about how
could I break this down?