Math CentralQuandaries & Queries


Question from morgan, a student:

Hi will you please help me with my math question

order the #s from least to greatest

18 7/12, 18 2/3, 183/4, 18 1/3 Please help

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

That's the answer. Now you try this method with your question.

Stephen La Rocque.

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