Difference between revisions of "2019 AMC 8 Problems/Problem 3"
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Contents
Problem 3
Which of the following is the correct order of the fractions and from least to greatest?
Solution 1
We take a common denominator:
Since it follows that the answer is .
xMidnightFirex
~ dolphin7  I took your idea and made it an explanation.
Solution 2
When and , . Hence, the answer is . ~ ryjs
This is also similar to Problem 20 on the AMC 2012.
Solution 3 (probably won't use this solution)
We use our insane mental calculator to find out that , , and . Thus, our answer is .
~~ by an insane math guy.
Solution 4
Suppose each fraction is expressed with denominator : . Clearly so the answer is .
Solution 5 SweetMango77
We notice that each of these fraction's numerator denominator . If we take each of the fractions, and subtract from each, we get , , and . These are easy to order because the numerators are the same, we get . Because it is a subtraction by a constant, in order to order them, we keep the inequality signs to get .
See also
2019 AMC 8 (Problems • Answer Key • Resources)  
Preceded by Problem 2 
Followed by Problem 4  
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25  
All AJHSME/AMC 8 Problems and Solutions 
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
The butterfly method is a method when you multiply the denominator of the second fraction and multiply it by the numerator from the first fraction.