welcome to math with mr. J in this video we're going to take a look at how to compare fractions and as you can see there are 4 comparisons on your screen and we're going to go through each of these 4 in order to get this down so let's jump right in to number 1 and for number one we have 3/8 and thirteen sixteenths so the first thing you want to do when comparing fractions check to see if they have a common denominator if so it'll be pretty easy to compare the two fractions if they do not have a common denominator we need to find one and rename those fractions that way it'll make it very easy to compare when we do have a common denominator so let's take a look we have three-eighths and thirteen sixteenths so obviously we don't have a common denominator there so we need to find one and rename and the common denominator for an 8 and a 16 is 16 so let's rename this first fraction and I'm going to do it underneath there where I wrote that 16 well I know 8 times 2 will give me 16 so in order to find an equivalent fraction we need to do the same thing to the top so 3 times 2 is going to give me 6 3/8 is equivalent to 6 sixteenths they hold the same value so I did not change the problem I just renamed with that common denominator the second fraction thirteen sixteenths already has a denominator of 16 so I do not need to rename or do anything to that fraction now that we have a common denominator it's very easy to compare and we can see that 6 16 is less than thirteen sixteenths right 13 out of 16 is going to be greater than 6 out of 16 so let's put our symbol in here and we can read that from left to right as 3/8 is less than thirteen sixteenths another way to think of this problem is you can see on the Left we have 3/8 right that's less than half because 1/2 is 4 eighths so the left side is less than 1/2 now on the right we have thirteen sixteenths and that's greater than 1/2 because half of 16 is 8 16 so the right side is more than 1/2 and the left side is less than 1/2 so we could tell by using that strategy or you can prove it by changing the denominators you know using a common denominator and renaming so let's take a look at number two here we have two twelve and eight nights we do not have a common denominator so let's find one and rename so four twelve and nine your common denominator is going to be 36 12 times 3 is 36 so let's do the same thing to the top 2 times 3 is 6 9 times 4 is 36 so do the same thing to the top 8 times 4 is 32 now that we have a common denominator and we renamed it's very easy to compare 630 sixths is less than 32 36 and let's take a look at the original problem again now 2 12 is less than 1/2 right because 6 out of 12 is 1/2 so obviously 2 out of 12 is less than 6 out of 12 so the left side is less than 1/2 and the right side 1/2 a 9 is 4 and 1/2 and we have 8 nights so we're well over half so the right side right off the bat we could see is more in half and the left side is less than half that can also help us compare but again we prove the comparison when we found a common denominator and renamed so let's take a look at number three now both of these fractions are over half so we can't use the benchmark strategy here with these fractions so we're going to need to find a common denominator and rename so 3/4 and 6/8 so we have a 4 and an 8 and our common denominator is going to be 8 now that second fraction 6/8 already has that denominator of 8 so we do not need to do anything we're going to leave it as is 3/4 okay we need to think well 4 times 2 gives me that denominator of 8 so I need to do the same thing to the top 3 times 2 gives me 6 so both sides are equivalent to 6/8 so both these fractions are equal so 3/4 is equal or equivalent to 6/8 let's take a look at number 4 and just using benchmarks and fractions sense when I talked about the 1/2 for numbers 1 2 & 3 that's a benchmark fraction that we can base different things off of so when I say the word benchmark I'm just talking about a fraction we can use to help us through these problems now eight tenths is above half right because half would be five tenths and on the right we have 17 twentieths well 1/2 a 20 is 10 so that one's above 1/2 as well so we can't really tell right off the bat which one's greater or less than so let's rename with a common denominator so we have a 10 and a 20 so our common denominator is going to be 20 now the second fraction 17 twentieths already has that denominator of 20 so we do not need to do anything to that fraction now the first one well 10 times 2 gives me the denominator of 20 so let's do the same thing to the top 8 times 2 is 16 now these fractions are very close in value but the 17 20th is 120th grader it's a little bit greater so let's read this left to right 8 tenths is less than 17 20th so there you have it there's how you compare fractions use benchmarks right use 1/2 to kind of judge where you're at with the fractions and then rename using common denominators in order to prove your answer thanks so much for watching until next time peace