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## 5th grade

### Course: 5th grade > Unit 6

Lesson 1: Multiplication as scaling# Fraction multiplication as scaling examples

Learn the concept of multiplication as scaling. Watch examples of how multiplying by a fraction scales a number up or down. Understand that fractions between zero and one make numbers smaller, while fractions greater than one make numbers larger.

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## Video transcript

- [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.