Main content

## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 3

Lesson 1: Multiplication intro- Multiplication as equal groups
- Intro to multiplication
- Basic multiplication
- Multiplication with arrays
- Understand multiplication using groups of objects
- Multiply with arrays
- Worked example: Whole numbers on the number line
- Represent multiplication on the number line
- More ways to multiply
- Ways to represent multiplication

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Multiplication with arrays

CCSS.Math:

Let's explore this video about representing 12 with multiplication. It shows 12 as 4x3, 3x4, 2x6, 6x2, 1x12, and 12x1. This helps students understand multiplication and different group arrangements. Created by Sal Khan.

## Want to join the conversation?

- is addition the same thing as multiplication(8 votes)
- In a way, yes.

Multiplication is simply a faster method of addition. When you multiply a number by another number, you are basically adding a number the same amount of times as the other number calls for, e.g: 5*3 = 5+5+5 and 3*5 = 3+3+3+3+3.

Hope this helps!(21 votes)

- how do you do multiplication(11 votes)
- you can do this 5x4=20(10 votes)

- why not show in this video, that making groups of 5 or 7 is not possible?(2 votes)
- It is possible, but in multiplication you always want even groups.(3 votes)

- What number comes after googlplex?(3 votes)
- Really any number that has one or more zeros can come after a googolplex because numbers exist into infinity but if you are asking what the largest named number is then it would be both a googolplexian and like Sajjad-Bin-Samad said the Graham's number.(7 votes)

- is this like a start to multiplication? If it is, why is it for third grade?(4 votes)
- Yes, groups of objects is the basic meaning of multiplication. Multiplication is taught in 3rd grade.

You don’t always have to draw groups of objects to multiply numbers, but it is good to mentally visualize groups of objects.

Have a blessed, wonderful day!(4 votes)

- so yore saying you multiply 3 groups of 4 3 times fore everything it would be 12?(4 votes)
- Yes it Will be 12(3 votes)

- who made math? by the way(5 votes)
- I hate these videos pls remove them(4 votes)
- this video is inchresting like you said(4 votes)
- what is 5,570+ what equals 250,000(3 votes)

## Video transcript

So, I have several groups of
these ball-looking things. And let's think about how
many balls are in each group. We have 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11 12. And what I want to do is
think about the different ways of dividing these 12 balls into
different numbers of groups. So, for example, I could
view these 12 balls as one, so that's 1 group of 3, 2
groups of 3, 3 groups of 3, 4 groups of 3. So I could view 12 as
being 4 groups of 3. And the way that
we would write that is that 12 is equal
to 4 groups of 3. Or another way of reading this
is that 12 is equal to 4 times 3. If I have 1, 2, 3, 4 groups,
and in each of those groups I have 1, 2, 3,
objects, I'm going to have a total of 12 objects. But that's not the only
way we can get to 12. We could also view
it as 3 groups of 4. So, let's look at that. So we could have it as 1
group of 4, 2 groups of 4, 3 groups of 4. So now we could view 12
as being 3 groups of 4. Or we could say-- let me get the
right tool out-- that 3 times 4 is equal to 12. So, whether we're doing
4 times 3 or 3 times 4, they're both going
to be equal to 12. 4 groups of 3 is
12, 3 groups of 4. But we don't have to stop there. We could also view
12 as, well, we could view it as 2 groups of 6. Let's look at that. So this is 1 group
of 6 right over here. So, that's one 1 of 6. That's another group of 6. So, once again, we could
view this as 2 times 6. 2 times 6 will also get us a 12. Well, what about doing
it as 6 groups of 2? Well, we can draw that
out, too-- 6 groups of 2. So that's 1 group of 2. Let me do that in
a different color. Let me do it in
this purple color. We have 1 group of 2, 2
groups of 2, 3 groups of 2, 4 groups of 2, 5 groups
of 2, and 6 groups of 2. So once again, this
is all different ways of writing 12, something
equivalent to 12. We could write 6 times 2--
6 groups of 2-- 6 times 2 is also equal 12. But we don't have to stop there. We could also literally
view 12 as 1 group of 12. So how would that look? So 1 group of 12. So this whole thing is
just 1 group of 12 here. So we could literally say
1 times 12 is equal to 12. We have one entire group of 12. 1 times 12 is equal to 12. And we could think of
it the other way around. We could view this
as 12 groups of 1. Let me draw that. So 12 groups of 1. This is 1 group of
1, 2 groups of 1, 3, 4, 5, 6, 7, 8, 9, 10,
11, and 12-- 12 groups of 1. So we could also write 12. 12 groups, and in
each one, I have 1. Well, that's still
going to get me to 12.