Difference between revisions of "2019 AMC 8 Problems/Problem 3"
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We use our insane mental calculator to find out that <math>\frac{15}{11} \approx 1.36</math>, <math>\frac{19}{15} \approx 1.27</math>, and <math>\frac{17}{13} \approx 1.31</math>. Thus, our answer is <math>\boxed{\textbf{(E)}\frac{19}{15}<\frac{17}{13}<\frac{15}{11}}</math>. | We use our insane mental calculator to find out that <math>\frac{15}{11} \approx 1.36</math>, <math>\frac{19}{15} \approx 1.27</math>, and <math>\frac{17}{13} \approx 1.31</math>. Thus, our answer is <math>\boxed{\textbf{(E)}\frac{19}{15}<\frac{17}{13}<\frac{15}{11}}</math>. | ||
− | ~~ by an insane math guy | + | ~~ by an insane math guy. |
==Solution 5== | ==Solution 5== |
Revision as of 13:14, 2 November 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.