Comparing fractions

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.