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## 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

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# Ways to represent multiplication

Sal explains different ways to represent 7 times 5. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- what is the trick for nines(54 votes)
- a really awesome way to multiply the 9 times tables really fast is to use your haands! literally! take 9x2 for example,spread out your fingers and pull down the 2nd closest finger to your left.On the right side of the separation is 8 fingers and the left has 1.Put the left amount of fingers down first (1),THEN put the right one(s) beside it.for 9x3,put the third finger closest to the left down.2 on the left,7 on the right and there is 27!this goes on and on till 10x9.9 on the left,0 on the right :90! this is a really long explanation but if you think about it ,you will litteraly have that knowledge ,"at your finger tips".(48 votes)

- why do you need to know multiple forms of the way to represent multiplication? Why can't you always just use "x"?(9 votes)
- Later on there will be variables, which are usually letters like x, so it might get a little confusing. For example 6 times x plus 1 times 2 times z minus could be represented as (6x+1)·(2x-4) because (6xx+1)x(2xz-4) would be a totally different operation. Parenthesis mean that the operation inside gets done first. Hope this helps.(3 votes)

- you can just memorize the times tables(5 votes)
- 2:42is a good part to watch to answer this question.(7 votes)

- does * (the star ) a multulication sign to(5 votes)
- Yes. * or "The Star" means a multiplication sign(3 votes)

- what is the trick for all numbers(3 votes)
- 14 x 2 = 2 x 14 = 28 right ?(2 votes)
- Yes that is correct and that is also called communicative property(2 votes)

- i am have trubles remember few multiplication tables(2 votes)
- Hello Teresa! The best way to remember your multiplication tables is practice. Making flash cards is one great way to do this. If you take a little amount of time out of each day I promise you that within just a few days you will start to find yourself remember your multiplication tables. I hope this helps! :)(2 votes)

- This helped me a lot, thanks!(2 votes)
- Rewrite 5 plus 5 plus 5 plus 5 plus 5 plus 5 plus 5 as a multiplication expression. And then they want us to write the expression three times using different ways to write multiplication. So let's do the first part. Let's write it as a multiplication expression. So how many times have we added 5 here? Well, we've got it at one, two, three, four, five, six, seven. So one way to think of it, if I just said what is here? How many 5's are there? You'd say, well, I added 5 to itself seven times, right? You could literally say this is 7 times 5. We could literally write, this is 7 times 5, or you could view it as 5 seven times. I'm not even writing it mathematically yet. I'm just saying, look, if I saw seven of something, you would literally say, if these were apples, you would say apples seven times, or you'd say seven times the apple, whatever it is. Now, in this case, we're actually adding the number to each other, and we could figure out what that is, and why don't we? But the way we would write this mathematically, we would say this is 7 times 5. We could also write it like this. We could write it 7 dot 5. This and this mean the exact same thing. It means we're multiplying 7 times 5 or 5 times 7. You can actually switch the order, and you get the exact same value. You could actually write it 5 times 7. So you could interpret this as 7 five times or 5 seven times, however you like to do it, or 5 seven times. I don't want to confuse you. I just want to show you that these are all equivalent. This is also equivalent. 5 times 7. Same thing. You could write them in parentheses. You could write it like this. This all means the same thing. That's 7 times 5, and so is this. These all evaluate to the same thing: 5 times 7. So these are all equivalent, and since we've worked with it so much, let's just figure out the answer. So if we add up 5 to itself seven times, what do we get? Well, 5 plus 5 is 10. 10 plus 5 is 15, plus 5 is 20, plus 5 is 25, plus 5 is 30, plus 5 is 35. So all of these evaluate to 35, just so you see that they're the same thing. These are all equivalent to 35. And just something to think about, this is also the exact same thing, depending on how you want to interpret this, as 7 five times. They didn't ask us to do it, but I thought I would point it out to you. 7 five times would look like this: 7 plus 7 plus 7 plus 7 plus 7, right? I have 7 five times. I added it to itself five different times. There's five 7's here added to each other. And when you add these up, you'll also get 35. And that's why 5 times 7 and 7 times 5 is the same thing.

Video on YouTu(2 votes) - Isn't the x used for multiplication confusing, since x can also be treated as a variable in algebra?(1 vote)
- Yeah, using "x" for multiplication is really confusing when your dealing with algebra. That is why in algebra we normally don't use "x" for multiplication. Instead we replace it with a dot.(3 votes)

## Video transcript

Rewrite 5 plus 5 plus 5 plus
5 plus 5 plus 5 plus 5 as a multiplication expression. And then they want us to write
the expression three times using different ways to
write multiplication. So let's do the first part. Let's write it as a
multiplication expression. So how many times have
we added 5 here? Well, we've got it at
one, two, three, four, five, six, seven. So one way to think of it, if
I just said what is here? How many 5's are there? You'd say, well, I added 5 to
itself seven times, right? You could literally say
this is 7 times 5. We could literally write, this
is 7 times 5, or you could view it as 5 seven times. I'm not even writing it
mathematically yet. I'm just saying, look, if I saw
seven of something, you would literally say, if these
were apples, you would say apples seven times, or you'd
say seven times the apple, whatever it is. Now, in this case, we're
actually adding the number to each other, and we could figure
out what that is, and why don't we? But the way we would write this
mathematically, we would say this is 7 times 5. We could also write
it like this. We could write it 7 dot 5. This and this mean the
exact same thing. It means we're multiplying
7 times 5 or 5 times 7. You can actually switch the
order, and you get the exact same value. You could actually write
it 5 times 7. So you could interpret this as 7
five times or 5 seven times, however you like to do
it, or 5 seven times. I don't want to confuse you. I just want to show you that
these are all equivalent. This is also equivalent. 5 times 7. Same thing. You could write them
in parentheses. You could write it like this. This all means the same thing. That's 7 times 5,
and so is this. These all evaluate to the
same thing: 5 times 7. So these are all equivalent, and
since we've worked with it so much, let's just figure
out the answer. So if we add up 5 to itself
seven times, what do we get? Well, 5 plus 5 is 10. 10 plus 5 is 15, plus 5 is 20,
plus 5 is 25, plus 5 is 30, plus 5 is 35. So all of these evaluate to
35, just so you see that they're the same thing. These are all equivalent
to 35. And just something to think
about, this is also the exact same thing, depending on how you
want to interpret this, as 7 five times. They didn't ask us to do it, but
I thought I would point it out to you. 7 five times would look like
this: 7 plus 7 plus 7 plus 7 plus 7, right? I have 7 five times. I added it to itself five
different times. There's five 7's here
added to each other. And when you add these up,
you'll also get 35. And that's why 5 times 7 and 7
times 5 is the same thing.