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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.

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.