Ways to represent multiplication
About this video
Sal rewrites 5 + 5 + 5 + 5 + 5 + 5 + 5 as the multiplication 7 x 5, and shows other ways to write it: with a dot (7 . 5), with parentheses, and as 5 x 7. All of them equal 35, and so does 7 added to itself five times.
You'll be able to
- rewrite repeated addition as a multiplication.
- write a multiplication with a times sign, a dot or parentheses.
- explain why 7 x 5 and 5 x 7 are equal.
Key words
- multiplication expression
- A maths phrase like 7 x 5 that shows numbers being multiplied.
- equivalent
- Having the same value, even if written differently.
- parentheses
- Round brackets ( ); two side by side, like (7)(5), mean multiply.
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.
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