Problem:
Which of the following is the correct order of the fractions 1115​, 1519​, 1317​, from least to greatest?
Answer Choices:
A. 1115​<1317​<1519​
B. 1115​<1519​<1317​
C. 1317​<1519​<1115​
D. 1519​<1115​<1317​
E. 1519​<1317​<1115​
Solution:
We can rewrite the fraction as follows:
1115​=1+114​,1317​=1+134​,1519​=1+154​.
Recall that if two fractions have the same numerator, then the fraction with the larger denominator is smaller. Using this fact, we can see that the correct ordering is
1519​<1317​<1115​.
Thus, the correct answer is E.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions