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order the fractions from least to greatest so we have three fractions and we want to decide which one is the smallest which ones 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 7/10 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 one-third we could say one of your 3 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 a 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 one-third but then we get over here two five six and five out of six well again that's most of the group but is this most of the group greater than the 7/10 most of the group that gets a 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 tenths 2/3 2/6 because those are all different sizes different sized groups different sized pieces that's tricky to compare so we want to change these to be the same size so we need some number a multiple of 10 3 & 6 something we can multiply 10 3 & 6 by to get a new denominator that will work for all of the fractions one way I like to figure this out is I look at the biggest denominator which is 10 and I think of its multiples the first multiple is 10 because 10 times 1 is 10 can we change thirds and sixths to have 10 as a denominator is there any whole number you can multiply 3 times to get 10 there's not so we need to keep going 10 doesn't work the next multiple of 10 is 10 times 2 which is 20 again 3 & 6 is they're a whole number we can multiply them by to get 20 again Oh so 20 doesn't work how about 30 let's see 3 we can multiply 3 times 10 to get 30 so 30 works for 3 how about 6 6 times 5 equals 30 so yes 30 can work to be our common denominator thirtieths 30 is a multiple of 10 3 & 6 so let's start converting our fractions to have denominators of 30 we'll start with 7 tenths and we wanted to have a denominator of 30 so what do we need to multiply by 10 times 3 is 30 we always multiply the numerator and denominator by the same number so 7 times 3 is 21 so 7/10 is equal to 21 xxx 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 a denominator of 30 so this time we'll multiply 3 times 10 to get 30 again numerator also times 10 1 times 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 5/6 what do we need to multiply here to get 30 6 times 5 is 30 so we multiply the numerator times 5 and 5 times 5 is 25 so now instead of these original fractions that were tricky to compare we have much easier numbers to compare we have 21 thirtieths 10 xxx and 25 thirtieths so in this case the pieces are all thirtieths 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 7/10 is the same as 21 out of 30 whereas 1/3 is 10 out of 30 well clearly 21 out of 30 is a 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 10 thirtieths which again remember is equal to 1/3 so we can put 1/3 is least and when you cross that off next it's either 21 out of 30 or 25 21 is less and that represented 7/10 so we can say 7/10 because 21 thirtieths equals 7/10 and finally that leaves us with 25 xxx which is equivalent to 5/6 so from least to greatest our fractions are 1 3 7 10 and then 5/6