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Multiplying mixed numbers by whole numbers

Sal uses repeated addition to help multiply a whole number by a mixed number.

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Video transcript

- [Instructor] Let's see if we can figure out what 2 1/4 times three is. Pause this video and see if you can work that out. All right, now there's different ways that we could approach this. One way to approach this is to recognize that if I multiply anything times three, that means that I'm taking three of these things and adding them together. So, this is going to be the same thing as 2 1/4 plus 2 1/4 plus 2 1/4. Now, I could also view this as each of these 2 1/4 is two plus 1/4 plus two plus 1/4 plus two plus 1/4. All I did is I broke up each of the 2 1/4 into a two plus 1/4. And then what I could do is I could add the whole number parts, two plus two plus two is going to be equal to six. And then, if I were to take 1/4 plus 1/4 plus 1/4, how many fourths do I now have? I have 3/4, so it's gonna be six plus 3/4, or I could write this as 6 3/4. Now, another way that we could have approached this is we could've rewritten 2 1/4. I could have rewritten that as the same thing as two is 8/4, 8/4 is the same thing as two, plus 1/4 and then I'm multiplying that whole thing times three. And so, this is going to be the same thing as 9/4, 8/4 plus 1/4 is 9/4, times three. And so, we could say, "Hey, that's just going to be equal "to 9/4 plus 9/4 plus 9/4, which would be equal to what?" Well, I have, this is going to be nine plus nine plus nine fourths, which is going to be equal to 27/4. Now, you might be saying, "Hey, these look like they are different", but you could check this. Six is equal to how many fourths? So, six is equal to 24/4, 24/4 plus 3/4, which is exactly equal to 27/4. And we are done.