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Welcome to my presentation
on equivalent fractions. So equivalent fractions
are, essentially what they sound like. They're two fractions that
although they use different numbers, they actually
represent the same thing. Let me show you an example. Let's say I had
the fraction 1/2. Why isn't it writing. Let me make sure I get
the right color here. Let's say I had
the fraction 1/2. So graphically, if we to draw
that, if I had a pie and I would have cut it
into two pieces. That's the denominator
there, 2. And then if I were to eat
1 of the 2 pieces I would have eaten 1/2 of this pie. Makes sense. Nothing too complicated there. Well, what if instead of
dividing the pie into two pieces, let me just draw
that same pie again. Instead of dividing it in two
pieces, what if I divided that pie into 4 pieces? So here in the denominator I
have a possibility of-- total of 4 pieces in the pie. And instead of eating one
piece, this time I actually ate 2 of the 4 pieces. Or I ate 2/4 of the pie. Well if we look at these two
pictures, we can see that I've eaten the same
amount of the pie. So these fractions
are the same thing. If someone told you that they
ate 1/2 of a pie or if they told you that they ate 2/4 of a
pie, it turns out of that they ate the same amount of pie. So that's why we're saying
those two fractions are equivalent. Another way, if we actually
had-- let's do another one. Let's say-- and that pie is
quite ugly, but let's assume it's the same type of pie. Let's say we divided
that pie into 8 pieces. And now, instead of eating 2
we ate 4 of those 8 pieces. So we ate 4 out of 8 pieces. Well, we still ended up eating
the same amount of the pie. We ate half of the pie. So we see that 1/2 will equal
2/4, and that equals 4/8. Now do you see a pattern here
if we just look at the numerical relationships
between 1/2, 2/4, and 4/8? Well, to go from 1/2 to 2/4 we
multiply the denominator-- the denominator just as review is
the number on the bottom of the fraction. We multiply the
denominator by 2. And when you multiply the
denominator by 2, we also multiply the numerator by 2. We did the same thing here. And that makes sense because
well, if I double the number of pieces in the pie, then I have
to eat twice as many pieces to eat the same amount of pie. Let's do some more examples
of equivalent fractions and hopefully it'll
hit the point home. Let me erase this. Why isn't it letting me erase? Let me use the regular mouse. OK, good. Sorry for that. So let's say I had
the fraction 3/5. Well, by the same principle,
as long as we multiply the numerator and the denominator
by the same numbers, we'll get an equivalent fraction. So if we multiply the numerator
times 7 and the denominator times 7, we'll get 21-- because
3 times 7 is 21-- over 35. And so 3/5 and 21/35 are
equivalent fractions. And we essentially, and I don't
know if you already know how to multiply fractions, but all we
did is we multiplied 3/5 times 7/7 to get 21/35. And if you look at this, what
we're doing here isn't magic. 7/7, well what's 7/7? If I had 7 pieces in a pie
and I were to eat 7 of them; I ate the whole pie. So 7/7, this is the
same thing as 1. So all we've essentially
said is well, 3/5 and we multiplied it times 1. Which is the same thing as 7/7. Oh boy, this thing
is messing up. And that's how we got 21/35. So it's interesting. All we did is multiply the
number by 1 and we know that any number times 1
is still that number. And all we did is we figured
out a different way of writing 21/35. Let's start with
a fraction 5/12. And I wanted to write that with
the denominator-- let's say I wanted to write that with
the denominator 36. Well, to go from 12 to 36, what
do we have to multiply by? Well 12 goes into
36 three times. So if we multiply the
denominator by 3, we also have to multiply the numerator by 3. Times 3. We get 15. So we get 15/36 is the
same thing as 5/12. And just going to our original
example, all that's saying is, if I had a pie with 12
pieces and I ate 5 of them. Let's say I did that. And then you had a pie, the
same size pie, you had a pie with 36 pieces and
you ate 15 of them. Then we actually ate the
same amount of pie.