Khan academy multiplying fractions by whole numbers

Video transcript

- [Voiceover] Rishi spend 3/4 of an hour for two days working on his science project. Kyle spent 1/4 of an hour for six days working on his science project. Who spent more time on his science project? So we wanna know who spent more time, and to do that we need to first know the amount of time Rishi and Kyle each spent on their science projects. So let's start with Rishi, and see what we know about Rishi. Rishi spent 3/4 of an hour for two days, so two times, he spent 3/4 of an hour. Or another way we could say this, is he spent 3/4 of an hour once, plus on a second day he spent another 3/4 of an hour. So 3/4 plus another 3/4 will give us a total of 6/4, or six quarter hours, that Rishi spent on his science project. Now let's look at Kyle. Kyle spent a 1/4 of an hour, so here's Kyle. Kyle spent 1/4 of an hour, but he did this for six days, so six times, he spent 1/4 of an hour. Or we could say that Kyle spent 1/4 of an hour one day, plus 1/4 of an hour a second day, 1/4 of an hour a third day, a fourth day, a fifth day, and then a sixth day he spent 1/4 of an hour. So six times, one, two, three, four, five, six, he spent a quarter, or 1/4 of an hour working on his project. So if we have six 1/4s, then we have a total of 6/4. So Kyle spent 6/4, or six quarter hours. And now back to our question, now that we know how much each of them spent, who spent more time working on his science project? Rishi with 6/4 hours, or Kyle with 6/4 hours? And the answer here, of course, is that these are equal, these are the same. Rishi and Kyle spent the same amount of time, so we could say the same amount of time working on each other their science projects.

Video transcript

So we have here, it says 2 times 4/3 is equal to 8 times blank. And what I encourage you to do is pause the video right now and try to think about what should go in this blank. So I'm assuming you've given your try. Now, let's think through this. So 2 times 4/3, we can literally view that as the same thing as-- if we rewrite the 4/3, this is the same thing as 2 times-- instead of writing 4/3 like this, I'm literally going to write it as four 1/3's. And I know it sounds like I just said the same thing over again. But I'm literally going to write 1/3 four times-- 1/3 plus 1/3 plus 1/3 plus 1/3. If you call each of these 1/3, you literally have four of them. This is four 1/3's. 2 times 4/3 is the same thing as 2 times, literally, four 1/3's. Now, what would this be? Well, this is going to be equal to-- let me just copy and paste this-- is going to be this two times. So copy, and then let me paste it. So that's one group of those 1/3's, of those four 1/3's, or one group of one of these four 1/3's. And then, we'll have another one. And then, we'll have another one. And we're going to add them together. That's literally 2 times 4/3. So let's add these together. Now what do we have? Well, we have a bunch of 1/3's. And we need to count them up. We have one, two, three, four, five, six , seven, eight 1/3's. This is literally equal to-- and we could, just to make it clear what I've just done, we could ignore the parentheses and just add up all of these things together. So that might make it a little bit clearer. So let me do that just to make it clear that I literally take-- I've taken eight 1/3's and I'm adding them together, which is the exact same thing as 8/3. So let me clear that, and let me clear that, let me clear that. And so this is literally, or this is clearly, or hopefully clearly, equal to 8 times 1/3. I have 8 1/3's there. So going back to the original question, what is this equal to? 2 times 4/3 is the same thing as 8 times 1/3. And we've already seen that 8 times 1/3, well, that's literally 8/3. So we could also write it like this-- 8 over 3. Let me do that 3 in that other color-- 8 over 3.

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.

How do you multiply fractions by whole numbers?

When you multiply a whole number the answers are the same?

How many mastery points do you get for multiply fractions?

What happens when you multiply mixed fractions?

How do you multiply a fractions by a whole number?