Multiplying mixed numbers

Let’s see if we can figure out what 2 and 1/4 times 3 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 and 1/4 plus 2 and 1/4 plus 2 and 1/4.

Now, I could also view this as each of these two and one-fourths is 2 plus 1/4 plus 2 plus 1/4 plus 2 plus 1/4. All I did is I broke up each of the two and one-fourths into a two plus one-fourth.

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 one-fourth plus one-fourth plus one-fourth, how many fourths do I now have? I have three fourths. So it's going to be six plus three fourths, or I could write this as six and three fourths.

Now, another way that we could have approached this is we could have rewritten 2 and 1/4. I could have rewritten that as the same thing as 2, which is eight fourths. Eight fourths is the same thing as two plus one fourth, and then I'm multiplying that whole thing times three.

So this is going to be the same thing as nine-fourths: eight-fourths plus one-fourth is nine-fourths times three. And so we could say, hey, that's just going to be equal to nine-fourths plus nine-fourths plus nine-fourths, which would be equal to what? Well, I have this going to be 9 plus 9 plus 9, 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 twenty-four fourths. Twenty-four fourths plus three-fourths, which is exactly equal to twenty-seven fourths. And we are done.