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Determine whether 30/45 and 54/81

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are equivalent fractions.

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Well, the easiest way I can think of doing this is to put

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both of these fractions into lowest possible terms, and

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then if they're the same fraction, then they're

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equivalent.

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So 30/45, what's the largest factor of both 30 and 45?

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15 will go into 30.

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It'll also go into 45.

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So this is the same thing.

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30 is 2 times 15 and 45 is 3 times 15.

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So we can divide both the numerator and the

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denominator by 15.

15
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So if we divide both the numerator and the denominator

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by 15, what happens?

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Well, this 15 divided by 15, they cancel out, this 15

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divided by 15 cancel out, and we'll just be left with 2/3.

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So 30/45 is the same thing as 2/3.

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It's equivalent to 2/3.

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2/3 is in lowest possible terms, or simplified form,

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however you want to think about it.

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Now, let's try to do 54/81.

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Now, let's see.

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Nothing really jumps out at me.

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Let's see, 9 is divisible into both of these.

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We could write 54 as being 6 times 9, and 81 is the same

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thing as 9 times 9.

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You can divide the numerator and the denominator by 9.

30
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So we could divide both of them by 9.

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9 divided by 9 is 1, 9 divided by 9 is 1, so we get this as

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being equal to 6/9.

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Now, let's see.

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6 is the same thing as 2 times 3.

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9 is the same thing as 3 times 3.

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We could just cancel these 3's out, or you could imagine this

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is the same thing as dividing both the numerator and the

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denominator by 3, or multiplying both the numerator

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and the denominator by 1/3.

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These are all equivalent.

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I could write divide by 3 or multiply by 1/3.

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Actually, let me write divide by 3.

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Let me write divide by 3 for now.

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I don't want to assume you know how to multiply

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fractions, because we're going to learn that in the future.

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So we're going to divide by 3.

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3 divided by 3 is just 1.

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3 divided by 3 is 1, and you're left with 2/3.

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So both of these fractions, when you simplify them, when

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you put them in simplified form, both end up being 2/3,

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so they are equivalent fractions.