Ordering fractions Math 4 th grade Khan Academy

order the fractions from least to greatest so we have three fractions and we want to decide which one is the smallest which one's in the middle and which is the greatest so one thing we could do is look at the fractions think about what they mean and then estimate 710s let's say maybe that could represent seven of your 10 friends are wearing blue jeans well that's most most of your friends are wearing blue jeans and then for one3 we could say one of your three teachers wears glasses well that's not most if only one of the three wears glasses that's not most of the group so here's fraction that represents most of the group here's one that doesn't so the most is probably greater these two we could compare by estimating and see that this one 7/10 is probably greater than 1/3 but then we get over here to 56 and five out of six well again that's most of the group but is this most of the group greater than the seven intense most of the group that gets lot trickier so what we can do is we can try to change these fractions to make them easier to compare so we don't have to compare tths to/ thirs to Six because those are all different sizes different size groups different size pieces that's tricky to compare so we want to change these to be the same size so we need some number multiple of 10 three and six something we can multiply 10 three and 6 by to get new denominator that will work for all of the fractions one way like to figure this out is look at the biggest denominator which is 10 and think of its multiples the first multiple is 10 cu 10 * 1 is 10 can we change thirds and six to have 10 as denominator is there any whole number you can multiply three times to get 10 there's not so we need to keep going 10 doesn't work the next multiple of 10 is 10 * 2 which is 20 again three and six is there whole number we can multiply them by to get 20 again no so 20 doesn't work how about 30 let's see three we can multiply 3 * 10 to get 30 so 30 works for three how about 6 6 * 5 = 30 so yes 30 can work to be our common denominator 30ths 30 is multiple of 10 3 and six so let's start converting our fractions to have denominators of 30 we'll start with 7/10 and we want it to have denominator of 30 so what do we need to multiply by 10 * 3 is 30 we always multiply the numerator and denominator by the same number so 7 * 3 is 21 so 710 is equal to 213th these are equal we've just changed the size of the group we've changed the denominator so that they will be easier to compare but we've not changed what portion of the group we're representing 7 out of 10 is the same portion as 21 out of 30 and then let's keep going with 1/3 again we want to denominator of 30 so this time we'll multiply 3 * 10 to get 30 again numerator also times 10 1 * 10 is 10 10 out of 30 is the same as 1/3 if you have 10 of the 30 people again we'll use the wear glasses example or 1/3 that is the same size of the group the same portion and finally 56 what do we need to multiply here to get 30 6 * 5 is 30 so we multiply the numerator Time 5 and 5 * 5 is 25 so now instead of these original fractions that were tricky to compare we have much easier numbers to compare we have 2 13ths 1030s and 25 30ths so in this case the pieces are all 30th they're all groups of 30 so this is much easier to compare we can simply look at the numerators to see what portion of those 30 the fraction represents so the first 710 is the same as 21 out of 30 whereas 1/3 is 10 out of 30 well clearly 21 out of 30 is larger portion of the group than 10 out of 30 so we were right when we estimated up here that 7/10 is larger than 1/3 but then the trickier one over here now we can see much more clearly 25 out of 30 is the greatest portion of the group 25 is more than the 10 or the 21 so we can list these now from least to greatest the least the smallest is 103th which again remember is equal to 1/3 so we can put 1/3 is least and we can cross that off next it's either 21 out of 30 or 25 21 is less and that represented 710 so we can say 710 cuz 213th equals 7/10 and finally that leaves us with 253 which is equivalent to 5 6 so from least to greatest our fractions are 1/3 710 and then 56