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 Math Central Quandaries & Queries

Hi Morgan.

Since they all have "18" in front, you can ignore that for now and just concentrate on the fraction part.

To compare fractions, you want to have a common denominator for them all, then you can just compare the numerators. Here's an example:

(a) 2 3/5,
(b) 2 7/15,
(c) 2 2/3,
(d) 2 2/5

First, I ignore the 2 out front, because those are all the same. Now I look at the fractions. The denominators are 5, 15, 3 and 5 again. What number do all of these divide into evenly? 15, because 5 goes into 15 evenly, so does 15 and so does 3. So I will make the common denominator 15.

The first fraction is 3/5. What do I have to do to change the denominator to 15? I have to multiply the 5 by 3. So if I do that to the bottom, I have to also multiply the top by 3. 3x3 = 9, so the first fraction 3/5 becomes 9/15.

The second fraction already is over 15, so there's nothing to do there.

The third fraction 2/3 has to be multiplied by 5 on the denominator to make 15. That means we multiply the top by 5 as well and get the fraction 10/15.

And the last fraction is 6/15.

Now I'll write them out again using the new fractions:
(a) 2 9/15
(b) 2 7/15
(c) 2 10/15
(d) 2 6/15

Now we just look at the numerators and put them in order:
(d) 2 6/15
(b) 2 7/15
(a) 2 9/15
(c) 2 10/15