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# Comparing fractions

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Determine whether
30/45 and 54/81 are equivalent fractions. Well, the easiest way I can
think of doing this is to put both of these fractions into
lowest possible terms, and then if they're the same
fraction, then they're equivalent. So 30/45, what's the largest
factor of both 30 and 45? 15 will go into 30. It'll also go into 45. So this is the same thing. 30 is 2 times 15 and
45 is 3 times 15. So we can divide both the
numerator and the denominator by 15. So if we divide both the
numerator and the denominator by 15, what happens? Well, this 15 divided by 15,
they cancel out, this 15 divided by 15 cancel out, and
we'll just be left with 2/3. So 30/45 is the same
thing as 2/3. It's equivalent to 2/3. 2/3 is in lowest possible terms,
or simplified form, however you want to
think about it. Now, let's try to do 54/81. Now, let's see. Nothing really jumps
out at me. Let's see, 9 is divisible
into both of these. We could write 54 as being 6
times 9, and 81 is the same thing as 9 times 9. You can divide the numerator
and the denominator by 9. So we could divide both
of them by 9. 9 divided by 9 is 1, 9 divided
by 9 is 1, so we get this as being equal to 6/9. Now, let's see. 6 is the same thing
as 2 times 3. 9 is the same thing
as 3 times 3. We could just cancel these 3's
out, or you could imagine this is the same thing as dividing
both the numerator and the denominator by 3, or multiplying
both the numerator and the denominator by 1/3. These are all equivalent. I could write divide by
3 or multiply by 1/3. Actually, let me write
divide by 3. Let me write divide
by 3 for now. I don't want to assume you
know how to multiply fractions, because we're going
to learn that in the future. So we're going to divide by 3. 3 divided by 3 is just 1. 3 divided by 3 is 1, and
you're left with 2/3. So both of these fractions, when
you simplify them, when you put them in simplified form,
both end up being 2/3, so they are equivalent
fractions.