2012 AMC 8 Problems/Problem 20
Problem
What is the correct ordering of the three numbers , , and , in increasing order?
Solution 1
The value of is . Now we give all the fractions a common denominator.
Ordering the fractions from least to greatest, we find that they are in the order listed. Therefore, our final answer is .
Solution 2
Instead of finding the LCD, we can subtract each fraction from to get a common numerator. Thus,
All three fractions have common numerator . Now it is obvious the order of the fractions. . Therefore, our answer is .
Solution 3
Change into ; And Therefore, our answer is .
Solution 4
When and , . Hence, the answer is . ~ ryjs
This is also similar to Problem 3 on the AMC 8 2019, but with the rule switched.
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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