Comparing fractions

determine whether thirty forty fifth and fifty four eighty firsts 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 over 45 30 over 45 what's the largest factor of both 30 and 45 the one I'd let's see 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 we can divide or 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 forty fifth is the same thing as two thirds it's equivalent to two thirds 2/3 is in lowest possible terms a lower or simplified form however you want to think about it now let's think about 54 let's try to do 54 over 81 54 over 81 now let's see and 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 can 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 over 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 threes 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 divided by 3 or multiply by 1/3 which is 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 just one 3/3 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 so they are equivalent fractions