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### Course: 3rd grade > Unit 1

Lesson 3: Multiplication as groups of objects# Multiplication as equal groups

Sal uses arrays and repeated addition to visualize multiplication. Created by Sal Khan.

## Want to join the conversation?

- can you multiply fractions?(35 votes)
- Yes you can! Just multiply the tops of both of the fractions then the bottoms, then simplify. Hope that helps!(29 votes)

- who first used multiplication and in which country?(12 votes)
- The oldest known multiplication tables were used by the Babylonians about
**Iraq**4000 years ago . But he early**Egyptians**were the first to discover multiplication and to use it effectively as well as teach it to one another.

The modern method of multiplication based on the Hindu–Arabic numeral system was first described by**Brahmagupta**(598 - died after 665) was an**Indian**mathematician and astronomer.

Brahmagupta gave rules for addition, subtraction, multiplication and division.(28 votes)

- Is it possible to multiply with powers?(13 votes)
- Yes, you just multiply the numbers, and then
**add**the exponents.

http://www.mathsisfun.com/algebra/variables-exponents-multiply.html

(go down to**Multiplying Variables with Exponents**)(12 votes)

- can you multiply a decimal?(11 votes)
- Sure!

As we know when you multiply, you would line up the numbers like this:

134

* 5

-------

670

Now if you wanted to multiply a decimal, it would look like this:

10.42

* 3

--------

31.26

See? You pretty much do the same thing! However, you may stumble across the the problem where you do not know where to put the decimal. You would move the decimal to where the place value of the numbers multiplied. For example, if you did 10.001 * 3 it would be 30.003. The decimal is in the thousandths place on the first number so the answer would have it go to the thousandths place.

But remember, there is an exception to this rule. If you did 10. 05 * 2 it would be 20.1. This may be confusing, because that is in the tenths place instead of the hundredths.

This is because 10.05 * 2 really is 20.10 but you would round off the zero because it is not needed.

ΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩΩ

This all may be confusing to grasp at first, but as you get better at math, this will make more and more sense. If you need more help, either reply or ask an adult.(10 votes)

- Can we multiply negative variables??(7 votes)
- Yes.

A negative times a negative is positive.

A positive times a negative is negative.

Ex.: (-5) x (-5) = 25

(-4) x 2 = -8(6 votes)

- But how do we multiply a four digit number by a four digit number?

example: 1234 times 5678(6 votes)- ...this is a basic video that just introduces the concept. You probably want to watch the multi-digit multiplication videos: https://www.khanacademy.org/math/arithmetic/multiplication-division/multi_digit_multiplication(5 votes)

- why is the place holder zero?(4 votes)
- Because zero is nothing to it just takes up a place.(7 votes)

- At0:50why do they do addition in multiplication?(5 votes)
- At0:50, they show you that multiplication is basically just a short form for repetitive addition. It's not that they are adding and multiplying, but that they show you that multiplying is a way to add on a larger scale.

Once you know how to multiply, you will no longer have to add the same number over and over again, like 3 + 3 + 3 + 3, you can just multiply 3 * 4 and get the same answer, 12.(2 votes)

- Why do two negatives make a positive? (When multiplied...)(3 votes)
- its sort of how it is, those are the "rules" i mean think about it, its like magnets, when the same sides are put together, they repel and cancel each other out. So 2 negatives would equal a positive. For example, -2 * -2 = 4, -9 * -3 = 27, and so on(4 votes)

- at3:31, why does he show us an addition sentence to explain the multiplication sentence(3 votes)
- Addition is like the cousin of multiplication, for example 3x3=9 that's the same as 3+3+3+3+3+3+3+3. That's why he showed you the addition sentence so it could help you do multiplication!(4 votes)

## Video transcript

I have these three star patches,
I guess you could call them, right over here. And so I could say, if I had
one group of three star patches, how many star patches do I have? So I literally have one
group of three star patches. Well, that means that I
have three star patches. 1, 2, 3. This is my one group of three. Now let's make it a little
bit more interesting. Let's say that I had two groups. Let's say that I had
two groups of three. So that's one group, and
then here's a second group. Here's two groups of three. So how many total star
patches do I have now? Well, I have two
groups of three. Or another way of thinking
about it is this is 3 plus 3. This is equal to 3 plus
3, which is equal to 6. So we see 1 times 3--
one group of 3 is 3. Two groups of 3, which is
literally two 3's, is 6. Let's make it even
more interesting. Let's have three groups of 3. Now, what is this
going to be equal to? Well, it's three groups of 3. So I could write this as
three groups, 3 times 3. And how many of these star
patches do I now have? Well, this is going
to be 3 plus 3 plus 3. It's going to be
3 plus 3 plus 3. Notice I have three 3's. I have two 3's. I have one 3. So this is 3 plus 3
plus 3 is equal to 9. And you can count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, or
you could just count by 3's. 3, 6, 9. And I think you see
where this is going. Let's keep incrementing it. Let's get four groups of 3. So let's think about
what 4 times 3 is. 1, 2, 3, and 4. This right over here
is four groups of 3. We could write this
down as 4 times 3, which is the same thing
as 3 plus 3 plus 3 plus 3. Notice I have four 3's. One 3, two 3's,
three 3's, four 3's. One 3, two 3's,
three 3's, four 3's. So we get 3, 6, 9, 12. So what I encourage
you to do now, now that the video is almost
over, is to keep going. I want you to figure out what
5 times 3 is, and 6 times 3, and 7 times 3, and 8 times 3,
and 9 times 3, and 10 times 3. And I'll give you a little hint. You don't always have to
draw the star patches, but it's nice to visualize it. We saw 4 times 3 is
literally four 3's. Well, 5 times 3 is
going to be five 3's. So 2, 3, 4, 5. Which is equal to
3, 6, 9, 12, 15. So I encourage you to think
about what all of these are after this video is done.