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# More on equivalent fractions

Video transcript

What I want to do in this
video is really digest the idea that if we have some fraction,
as long as we multiply the numerator and the
denominator of the fraction by the same number,
then we're going to have an equivalent fraction. So let's think about that. Let's say we multiply the
denominator here by 2. I'm claiming that as long as
we multiply the numerator by 2, we are going to get an
equivalent fraction. So here, the denominator was 6. So here, our
denominator will be 12. If our numerator here
is 4, well, we've got to multiply by 2 again,
multiply our numerator by 2, to get 8. So I'm claiming that 8/12
is the same fraction as 4/6. And to visualize that,
let me redraw this whole. But instead of having
6 equal sections, we now have 12 equal sections. So each of the six
we can turn into 2. That's essentially what
multiplying by 2 does. We now have twice as
many equal sections. Now that we have twice as many
equal sections-- literally one, two, three, four, five, six,
seven, eight, nine, 10, 11 12-- how many of them are
actually shaded in yellow? Well, one, two three, four
five, six, seven, eight-- 8/12. And there's no magic here. If we have twice
as many sections, we're going to have to shade
in twice as many of them in order to have the same
fraction of the whole. And it goes the other way, too. This isn't just true
with multiplication. It's also true that if
we divide the numerator and the denominator
by the same quantity, we are going to have
an equivalent fraction. So that's another
way of saying, well, what happens if I
were to divide by 2? So if I were to divide by
2-- so let me divide by 2-- I'm going to have 1/2 the
number of equal sections. Or I will only have
three equal sections. And I'm claiming if I do the
same thing in the numerator, that this is going to
represent the same fraction. So 4 divided by 2 is 2. So I'm claiming that
2/3 is the same fraction as 4/6 is the same
fraction as 8/12. Well, let's visualize that. So here, this is
6 equal sections. But now, we're going to have
only three equal sections. So we can merge some of
these equal sections. So we can merge these
two right over here. And we can merge these
two right over here. And then, we can merge
these two right over here. So our whole is
still the same whole. But now, we only have
three equal sections. And two of them are
actually shaded in. So these are all
equivalent fractions. So the big takeaway here
is start with a fraction. If you multiply the
numerator and the denominator by the same quantity,
you're going to have an equivalent fraction. If you divide the numerator
and the denominator by the same
quantity, you're also going to have an
equivalent fraction. So with that in our brains,
let's tackle a little bit of an equivalent
fractions problem. Let's think about-- if
someone says, OK, I have 5/25, and I want to write that as some
value, let's call that value t, over 100, what would t be? Well, we can see
in the denominator to go from 25 to 100,
you had to multiply by 4. So if you want an
equivalent fraction, you have to multiply the
numerator by 4 as well. So t will need to
be equal to 20. So t is equal to 20. 5/25 is the same
thing as 20/100. But what if someone says, well,
5/25 is equivalent to blank, let's say question mark, over 5? Well now what would you do? Actually, let's do
it the other way-- is equal to 1 over
question mark. Well, you could say, look, to
get our numerator from 5 to 1, we have to divide by 5. We have to divide by
5 to go from 5 to 1. And so similarly, we have to
divide the denominator by 5. So if you divide the denominator
by 5, 25 divided by 5 is going to get you 5. So these are all
equivalent fractions. 1/5 is equivalent to 5/25,
which is equal to 20/100.