Fraction multiplication as scaling examples

- [Instructor] This right over here is an image from an exercise on Khan Academy and it says compare using greater than, less than, or equal to. And on the left, we have 1/4 times 5,000, and we wanna compare that to 5,000. On Khan Academy, you would click on this drop-down and you would pick greater than, less than, or equal to. So what do you think it is? How does 1/4 times 5,000 compare to 5,000? And how do you know your answer is correct? Pick one of these choices as well. Pause the video and have a go at that. Well, one way to think about it, if I'm multiplying 5,000 times some value, that value is going to scale 5,000. It's going to make it smaller or bigger or in certain cases, might not change the size at all. In fact, the ones where you don't change 5,000 was you multiply it by one. So one times 5,000 is equal to 5,000. But what do you think is going to happen when you multiply a value that is between zero and one times 5,000? Is that going to be greater than, equal to, or less than 5,000? Well one way to imagine it is on a number line. If this is zero, this is 5,000. This would be halfway between zero and 5,000. And if I then make it the space between zero and 5,000 into fourths, this would be 1/4 of the way between zero and 5,000. So this value right over here, that is 1/4 times 5,000. Well, how does this value, 1/4 times 5,000, compare to this value, to 5,000? Well, it's clear that 1/4 times 5,000 is less than, is less than 5,000. And in general, if the value is between zero and one that you're multiplying by something else, it's going to make the thing you're multiplying smaller. If this were one, it's not going to change the value. And if this were greater than one, it would make it larger. So let's see these choices. Because we are multiplying 5,000 by a fraction that is less than one. Yeah, that's exactly what's happening. We're multiplying 5,000 by 1/4. So it's going to give us a smaller value than 5,000. I like that choice. Let's just read these other ones. Because we are multiplying 5,000 by a fraction that is equal to one. Well no, 1/4 is clearly not equal to one, so we rule that one out. Because we are multiplying 5,000 by a fraction that is greater than one. Well 1/4 is clearly not greater than one, so we rule that out as well. Let's do another example. So here we're asked, is the product of each expression less than, equal to, or greater than 49? So pause this video and try to figure it out. All right, so this first one is 49 times 7/8. So what do you think that's going to be? Well, 7/8 is less than one. So if I multiply 49 times something less than one, I'm going to get a value that is less than 49. So I like that choice right over there. 49 times 5/2. Well, 5/2 is greater than one. Remember, 2/2 would be equal to one. So 5/2 is greater than one. So if I'm multiplying 49 by a value that is greater than one, I'm going to get a value that is greater than 49. And then last but not least, 49 times 3/3. Well, 3/3 is exactly equal to one. So 49 times one is going to be exactly equal to 49, and we're done.