Answer: Choice D) 14/23 > 5/9
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Convert each fraction shown to decimal form
- 5/9 = 0.55555
- 7/16 = 0.43750
- 8/15 = 0.53333
- 6/11 = 0.54545
- 14/23 = 0.60870
With the exception of 7/16 = 0.43750, the other decimal values are approximate.
From that list, we can see the decimal representations of 7/16, 8/15, and 6/11 are all smaller than the decimal version of 5/9. So we rule out choices A, B, and C. The answer must be choice D.
Sure enough, 14/23 = 0.60870 is indeed larger than 5/9 = 0.55555
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We can show this another way:
First off, assume that 14/23 and 5/9 are equal. We'll cross multiply and show a contradiction happens
14/23 = 5/9
14*9 = 23*5
126 = 115
The contradiction happens since we should get the same value on both sides if the two sides were equal, but they're not equal.
If we replace each equal sign with a greater than sign, then we get,
14/23 > 5/9
14*9 > 23*5
126 > 115
You can think of it like working backwards up the chain.
