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## 3rd grade

### Course: 3rd grade > Unit 1

Lesson 3: Multiplication as groups of objects# More ways to multiply

Sal uses arrays and repeated addition to multiply. Created by Sal Khan.

## Want to join the conversation?

- hi sal, ive learnt soo much from you, I'm not that good with math but after joining khan academy I know how to multiply 10s, 100s, ect. add, subtract, and decimals, but I am really struggling to memorise the multiplication table, any tips?(73 votes)
- well write it down a few times that is how i learned it.(30 votes)

- What if you have 0 group(20 votes)
- Its just 0 because that is kind of like a 0(15 votes)

- Why learn multiplication other ways? Like, it's harder memorizing other stratedies

why not just stick with one?(1 vote)- if you know other ways,then it will be easier to figure the answer. For example,if one person knows long multiplication and another person knows long multiplication AND a mental strategy, the second person will be more successful in math because he knows a mental strategy,which makes the question easier to figure out.(2 votes)

- Is division the inverse of multiplacation?(1 vote)
- Yes, division is the inverse of multiplication.(1 vote)

- How do I study my multiplication tables?(1 vote)
- You could try setting out a grid of questions and answers on graph paper, so that you number the squares from 1 to 12 going down the left side of the paper and across the top. Then you can fill in the open squares based on multiplying the number on the far left of the row and the number at the top of the column. Practice with the grid and then occasionally try to recreate the grid from memory until you can do it all.(1 vote)

- How do you know which number represents the groups and which number represents how many groups?(1 vote)
- It's the same number, but Crazy Donutz's question is reasonable,. In real life it may matter. If you have 5 packet of biscuits with 6 biscuits in each, you can share the biscuits equally between 6 friends only if you open the packages. It is only for exercises with text that it will matter, though, and there you will be told what you need to know.. A typical example is an exercise where you need to find how many liters of paint you need to buy when you can only buy full liters, and each liter covers a certain number of square meters. In this example you usually end up buying more than you need for the paint job..(1 vote)

- so addition and multiplication are similar in a way. but what about subtraction and division? do they have some relation with each other like the others?(1 vote)
- No, multiplication is the opposite of division, and thats the only relation I know about division

sorry if this didnt help(1 vote)

- Does multiplication have reminders?(1 vote)
- Multiplication between two whole numbers cannot have a remainder. The remainder is a unique property of division. If I ask you how many times does 3 go into 14 (i.e. what is 14/3) you could say that 3 goes into 14 4 times. But 3*4 is only 12. Therefore the remainder of the quotient is 2. There is nothing analogous to this in multiplication.(1 vote)

- what if you don't know how to skip count by 8 than what do you do?(1 vote)
- Remember that 8 is the same as 2 groups of 4. (8 = 2 x 4) If you can't count by groups of 8, try counting by groups of 4. If that is still too hard, try counting by groups of 2 and work your way up to counting by larger numbers.(0 votes)

- how is multiplication like repeated addition(1 vote)
- If you do: 7 + 7 + 7 + 7 = 28

you get the same result as 4 x 7 = 28

Multiplication is shorthand for repetitive addition.(1 vote)

## Video transcript

If we have 2 groups and
in each group I have 4, so that's one group
of 4, and then here is my second
group of 4, we already know that we could
write this as 2 times 4, which is the same
thing as 4 plus 4. Notice I have two 4's here. I have 4 plus another 4. Well, if I have 4 plus 4,
or if I have 2 groups of 4, either way, I'm going to
have a total of 8 things. And you see that
right over here. We have 1, 2, 3, 4,
5, 6, 7, 8 things. What I want you to do
is pause the video now and try to group these
same 8 things, but to group it in other ways so
that we can represent 8 as the product of whole numbers. Here I've represented 8
as the product of 2 and 4. 2 times 4 is 8. See if you can represent
8 as the product of other whole numbers,
or as whole numbers in different ways, grouping
it in different ways. So I assume you've
paused the video. So let's try it out ourselves. So one thing we
could do, we could view this instead
of as 2 groups of 4, we can view 8 as 4 groups of 2. So that's 1 group of 2, 2
groups of 2, 3 groups of 2, 4 groups of 2. So we could write that
4 times 2 is equal to 8. And we could view this as
the same thing as, literally, 4 2's. We have one 1, 2, 3, 4 2's. Each of these have 2 in them. So we're going to
say 1, 2, 3, 4 2's. 2 plus 2, plus 2,
plus 2 is equal to 8. These are both equivalent. 4 times 2, literally
4 groups of 2. That's the same thing as taking
4 2's and adding them together. Notice, we have 2
2's right over here. We added them together, 1, 2. Here, we have 4 2's
and we're adding them together, 1, 2, 3, 4. We take our 4 2's and
we add them together. How else could we represent 8? Well, we literally could
view it as 8 groups of 1. So let's do that. So 8 groups of 1
would look like this. That's 1 group of 1,
2, 3, 4, 5, 6, 7, 8. So we could write this
down as 8 times 1. 8 times 1 is, once
again, equal to 8. And if we wanted to write this
down as repeated addition, well, this is literally 8 1's. So 1 plus 1, plus 1,
plus 1, plus 1, plus 1. Let's see. That's 1, 2, 3, 4, 5, 6, 7, 8. 1, 2, 3, 4, 5, 6, 7, 8. 1 plus 1, plus 1, plus 1,
plus 1, plus 1, plus 1, plus 1 is equal to 8. Now, you might be
a little stumped. Well, what's another
way of getting to 8? Well, you could literally
view it as 1 group of 8. So let me view it that way. So this is just 1 entire
group of 8, the whole thing. The whole thing is a group of 8. So let me scroll over to
the right a little bit. We could write this
down as 1 times 8. And 1 times 8 is equal to 8. And how would we view that? Well, we only have one 8 now. We don't have to add that
one 8 to anything else. So if we wanted to do it the
way we've done the last few, we could literally write it
down as we just have one 8. Well, one 8 is clearly
going to just be equal to 8. So now let me ask
you another question. So far we've been focused
on each of these groups, but what if we actually
view this as 4 groups of 8. Then how many things are
we actually going to have? So let me make this very clear. So we have 1 group of eight 8,
2 groups of 8, 3 groups of 8, and 4 groups of 8. So we would view this
as 4 times 8, or which is going to be the same thing
as 8 plus 8, plus 8, plus 8. 4 8's. What is this going
to be equal to? A And I encourage you
to pause the video and figure it out right now. Well, there's a couple
of ways that you could have thought about this. You could have literally
just counted these. Or you could say, well, let's
see, you can skip count by 8. 8, 16, 24, 32. Or you could have said, 8
plus 8 is 16, plus 8 is 24, plus 8 is 32. Or you could have literally
just counted the triangles here.