Difference between revisions of "2019 AMC 8 Problems/Problem 3"
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Suppose each fraction is expressed with denominator <math>2145</math>: <math>\frac{2925}{2145}, \frac{2717}{2145}, \frac{2805}{2145}</math>. Clearly <math>2717<2805<2925</math> so the answer is <math>\boxed{\textbf{(E)}}</math>. | Suppose each fraction is expressed with denominator <math>2145</math>: <math>\frac{2925}{2145}, \frac{2717}{2145}, \frac{2805}{2145}</math>. Clearly <math>2717<2805<2925</math> so the answer is <math>\boxed{\textbf{(E)}}</math>. | ||
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{{AMC8 box|year=2019|num-b=2|num-a=4}} | {{AMC8 box|year=2019|num-b=2|num-a=4}} | ||
{{MAA Notice}} 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. | {{MAA Notice}} 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. |
Revision as of 19:48, 28 October 2020
Contents
Problem 3
Which of the following is the correct order of the fractions and from least to greatest?
Solution 1
Each one is in the form so we are really comparing and where you can see so the answer is .
Solution 2
We take a common denominator:
Since it follows that the answer is .
-xMidnightFirex
~ dolphin7 - I took your idea and made it an explanation.
Solution 3
When and , . Hence, the answer is . ~ ryjs
This is also similar to Problem 20 on the AMC 2012.
Solution 4(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 5
Suppose each fraction is expressed with denominator : . Clearly so the answer is .
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.