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Equivalent fractions on number lines

Sal uses a number line to help identify equivalent fractions with different denominators.  

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Video transcript

- [Instructor] So they are telling us that r fifths is equal to eight tenths and we need to figure out what is r going to be equal to and they help us out with this number line where they've put eight tenths on the number line. That makes sense because to go from zero to one, they've split it into one, two, three, four, five, six, seven, eight, nine, ten equal jumps and at this point, we have gone eight of those ten equal jumps between zero and one so that is eight tenths and they've also labeled one fifth for us and one way to think about it is if we look at these bold lines, zero, one, two, three, four, five, if you just look at the purple, we have five equal jumps. So each of those jumps are a fifth and so it makes sense that our first jump right over here gets us to one fifth and you can see that that is equivalent to two of the tenths. I'll just write that up here so we can see that equivalence. One fifth is equal to two tenths but how many fifths is equal to eight tenths? Pause this video and try to figure it out. All right, well this is one fifth. If we do one more jump of a fifth, that would be two fifths. Then if we go another fifth, that will get us to three fifths and then if we go another fifth, that will get us to four fifths which we see is exactly equivalent to eight tenths and that makes sense because we also saw that every fifth is equivalent to two tenths. So four fifths is going to be equivalent to eight of those tenths. We see that very clearly right over here and so r is equal to four. Four fifths is equal to eight tenths. So r is equal to four. Let's do another example. What fraction is equivalent to point A? So pause this video and see if you can figure that out. All right, so let's figure out where point A is. So to go from zero to one, we have one, two, three, four, five, six equal jumps. So each of these jumps are a sixth. So going from zero, one jump will get us to one sixth, then two sixths, then three sixths, then four sixths, then five sixths and so can we see four sixths in the choices? No I do not see four sixths. So we have to find an equivalent fraction to four sixths. So we could go choice by choice. The first choice has five sixths. Well we very clearly see that five sixths would be here on the number line which is clearly a different place than four sixths. So we could rule out this first choice but what about these other ones? Let's see, let's see how we can think about. Four fifths versus four sixths. Could those be equivalent? If I have four out of five versus four out of six, that's not feeling too good so I'm gonna put like a curly line through it. That's not feeling right, that if I could have four out of five equal jumps or five equal sections, that that would be the same as four out of six equal sections. If I divided it into six equal sections, each of those sections are going to be a little bit smaller than if I divided into five equal sections. So if I have four of each, they're going to be a different value. Actually when I talk it out like that, I feel even more confident that I could rule this one out. Now what about six fourths? Well one way to think about it is four fourths would be equal to one. So six fourths is going to be beyond one. So it's definitely not going to be where A is, so I could rule that one out and we could say oh, well maybe it's just going to be D but let's make sure that this makes sense. Two thirds, what does two thirds look like? Well let me try to divide this part of the number line from zero to one into thirds, into three equal sections. So I have zero there and then that could be one third, two thirds and then three thirds. That looks like three equal sections. So this is one third, this is two thirds, I'm making another jump of a third and then when I get to one, of course that is three thirds or we could have said six sixths and so point A, which is right over here I'm writing over it, that is indeed equal to two thirds. You can see each jump of a third is equal to two sixths. So it makes sense that four sixths is equal to two thirds or that two thirds is equal to four sixths so I like this one.