A very similar question is

http://800score.com/forum/viewtopic.php?t=128.

Which of the following fractions is the largest?

A. 11/14

B. 4/5

C. 9/14

D. 7/10

E. 5/6

(E) One way to solve this type of problem is to find the lowest common denominator for all of the fractions.To do this, first factor all of the denominators:

11/14: 14 factors into 2 and 7

4/5: 5 is prime

17/21: 21 factors into 3 and 7

29/35: 35 factors into 5 and 7

5/6: 6 factors into 2 and 3.

Then, to get a common denominator, we make sure that each of the factors is represented exactly once (since no factor is raised to a power in any denominator):

2 × 3 × 5 × 7 = 210.

Therefore, 210 is the lowest common denominator. Now we can express all the fractions in terms of the common denominator of 210 to see which is the largest:

11/14 × 15/15 = 165/210

4/5 × 42/42 = 168/210

9/14 × 15/15 = 135/210

7/10 × 21/21 = 147/210

5/6 × 35/35 = 175/210.

Therefore, 5/6 is the largest (175/210). The correct answer is choice (E).

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**I don't understand how you arrived at 15/15 , 42/42, 15/15 , 21/21, 35/35.**

Can you please explain further.