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## Comparing fractions of different wholes

## Video transcript

I want to make a
quick clarification based on the last video. In the last video, we
compared fractions. For example, we
compared 4/7 to 3/7. And we saw, clearly,
4/7 is a larger fraction of the
whole than 3/7 was. But you might say, hey, but
what if my whole was bigger? What if I took 3/7 of
this big thing here? Then 3/7 would look like this. So it would be 1, 2, 3/7. And so this 3/7--
this looks like I have filled in more than I would
have over here for the 4/7. So doesn't it matter which whole
you're taking the fraction of? And the answer is yes. It does matter. And when you compare
fractions, you assume that you're taking
fractions of the same whole. So you can only make this
comparison right over here. So it has to be-- let
me make this very clear. It has to be the same. It has to be the same whole that
you're making the comparison. You can't compare 4/7 of a
mouse to 3/7 of an elephant. Those are two different things. You cannot make that comparison. You could compare 4/7 of a
mouse to 3/7 of that same mouse, or a mouse the same size. Then you could make
the same comparison. When we talk about fractions
as just pure numbers, then we automatically
go to the number line. The whole that we talk about
when we're on the number line is the section of our
number line between 0 and 1. So if this is 0 and
then this is 1 here, when we talk about fractions
as just pure numbers, we're not saying 4/7 of a
mouse or 4/7 of an elephant. We're just talking about a
number on the number line. And so we would split
this into sevenths. Let me see if I could do that. Let me draw-- so that's
1/7, 2/7, 3/7, 4, 5, 6, and that's 7/7 right
over there, or 1. So this is 7/7, or 1. And this right over here is 1/7,
2/7, 3/7, 4/7, 5/7, and 6/7. And so when you look at
the number line here, it's clear that 3/7, which
is three jumps from 0, three jumps of a
seventh each-- 1, 2, 3-- 3/7 puts you right there,
while 4/7 is a larger number. It's to the right of 3/7. You have to make
four jumps-- 1, 2, 3, 4-- four jumps of a seventh
to get right over there. So you can make this
comparison as long as you're looking at the
fraction of the same whole. Here, the same
whole is the region of our number line
between 0 and 1. In the previous video, the
same whole was this yellow bar. You can't compare 4/7
of this yellow bar to 3/7 of this much
larger blue bar.