A very similar question is

http://800score.com/forum/viewtopic.php?t=74.

Which of the following fractions is the largest?

A. 11/14

B. 4/5

C. 17/21

D. 29/35

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 largest:

11/14 × 15/15 = 165/210

4/5 × 42/42 = 168/210

17/21 × 10/10 = 170/210

29/35 × 6/6 = 174/210

5/6 × 35/35 =

**175/210**.

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

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**Is there a faster way to solve this problem rather than trying to find the common denominator? That method takes too long. Any help is appreciated.**