I need to order 3/11, 1/8, 2/9 from least to greatest

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Question from Andrew, a student:

I need some help with my math home work and it is way to hard i am a sixth grader.
I need to order 3/11, 1/8, 2/9 in least to greatest. My teacher said you can find a common denominator
by multiplying the denominators. That was 792 That will take soo long i don't even know what 792
goes into eleven how many times their has to be an easier way please tell me if you know since i won't hear back from you for a long time because your busy people I should go try to figure it out the hard way. Oh and one more thing if you can this might be easier please teach me how to cross multiply with three # thank you.

-andrew

Hi Andrew,

I don't at all think this is too hard for a sixth grader, but you are making it harder than it need be. You can find a common denominator by multiplying the denominators as your teacher told you. Thus a common denominator is

11 × 8 × 9

I am not going to multiply these numbers since, as you will see in a minute, it is easier to work with 11 × 8 × 9.

Now express each fraction with the denominator 11 × 8 × 9. For the first fraction 3/11 you need to divide 11 into 11 × 8 × 9. Now it's easy, (11 × 8 × 9)/11 = 8 × 9 = 72.

Thus 3/11= (3 × 72)/(11 × 8 × 9) = 216/(11 × 8 × 9).

Similarly (11 × 8 × 9)/8 = 11 × 9 = 99 so

1/8 = 99/(11 × 8 × 9).

Express 2/9 as a fraction with denominator 11 × 8 × 9 and then it's straightforward to order the three fractions.

I hope this helps,
Penny

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