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# Ordering fractions

CCSS Math: 4.NF.A.2

## Video transcript

- [Voiceover] Order the
fractions from least to greatest. So we have three fractions, and we wanna 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. 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 1/3, 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 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 1/3. But then we get over here to 5/6, and five out of six, well, again, that's most of the group, but is this most of the group greater than the seven
tenths 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 10ths to thirds to sixths because those
are all different sizes, different sized groups,
different sized pieces, that's tricky to compare. So we wanna change these
to be the same size. So we need some number, a
multiple of 10, three, and six, something we can multiply
10, three, and six 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,
cause 10 times one is 10. Can we change thirds and sixths to have 10 as a 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 times two, which is 20. Again, three and six,
is there a 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 multiple three times 10 to get 30, so 30 works for three. How about six? Six times five equals 30, so yes. 30 can work to be our common denominator. 30ths, 30 is a multiple
of 10, three, 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
a denominator of 30, so what do we need to multiply by? 10 times three is 30. We always multiply the
numerator and denominator by the same number. So seven times three is 21. So 7/10 is equal to 21/30. 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. Seven 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 three times 10 to get 30. Again, numerator also times 10. One 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? Six times five is 30, so we multiply the numerator times five, and five times five is 25. So now, instead of
these original fractions that were tricky to compare, we have much easier numbers to compare. We have 21/30, 10/30, and 25/30. So in this case, the pieces are all 30ths. 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 10/30, which again, remember, is equal to 1/3. So we can put 1/3 is least, and we 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, 'cause 21/30 equals 7/10, and finally that leaves us with 25/30, which is equivalent to 5/6. So from least to greatest, our fractions are 1/3, 7/10, and then 5/6.