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Rewrite 5 plus 5 plus 5 plus 5 plus 5 plus 5 plus 5 as a

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multiplication expression.

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And then they want us to write the expression three times

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using different ways to write multiplication.

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So let's do the first part.

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Let's write it as a multiplication expression.

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So how many times have we added 5 here?

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Well, we've got it at one, two, three,

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four, five, six, seven.

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So one way to think of it, if I just said what is here?

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How many 5's are there?

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You'd say, well, I added 5 to itself seven times, right?

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You could literally say this is 7 times 5.

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We could literally write, this is 7 times 5, or you could

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view it as 5 seven times.

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I'm not even writing it mathematically yet.

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I'm just saying, look, if I saw seven of something, you

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would literally say, if these were apples, you would say

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apples seven times, or you'd say seven times the apple,

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whatever it is.

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Now, in this case, we're actually adding the number to

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each other, and we could figure out what that is, and

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why don't we?

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But the way we would write this mathematically, we would

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say this is 7 times 5.

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We could also write it like this.

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We could write it 7 dot 5.

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This and this mean the exact same thing.

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It means we're multiplying 7 times 5 or 5 times 7.

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You can actually switch the order, and you get the exact

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same value.

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You could actually write it 5 times 7.

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So you could interpret this as 7 five times or 5 seven times,

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however you like to do it, or 5 seven times.

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I don't want to confuse you.

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I just want to show you that these are all equivalent.

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This is also equivalent.

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5 times 7.

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Same thing.

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You could write them in parentheses.

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You could write it like this.

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This all means the same thing.

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That's 7 times 5, and so is this.

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These all evaluate to the same thing: 5 times 7.

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So these are all equivalent, and since we've worked with it

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so much, let's just figure out the answer.

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So if we add up 5 to itself seven times, what do we get?

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Well, 5 plus 5 is 10.

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10 plus 5 is 15, plus 5 is 20, plus 5 is 25, plus 5 is 30,

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plus 5 is 35.

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So all of these evaluate to 35, just so you see that

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they're the same thing.

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These are all equivalent to 35.

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And just something to think about, this is also the exact

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same thing, depending on how you want to interpret this, as

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7 five times.

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They didn't ask us to do it, but I thought I would point it

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out to you.

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7 five times would look like this: 7 plus 7 plus 7 plus 7

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plus 7, right?

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I have 7 five times.

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I added it to itself five different times.

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There's five 7's here added to each other.

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And when you add these up, you'll also get 35.

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And that's why 5 times 7 and 7 times 5 is the same thing.

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