All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
The Sum of the Parts Is Less Than And More Than the Parts (Posted on 2004-10-15) Difficulty: 2 of 5
Given a number of different fractions, create a new fraction whose numerator is the sum of all those fractions' numerators and whose denominator is the sum of the denominators. Call it y. Call the smallest of the original fractions x and the largest z.

Prove that for all cases, x < y < z.

No Solution Yet Submitted by Victor Zapana    
Rating: 2.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Practical use | Comment 8 of 11 |

As every student who properly understands the grading system most teachers use, adding the numerators and denominators of fractions is a way of averaging them.  The higher the denominator, the more the fraction is weighted.

For example, if you get 49/50 on a quiz and 94/100 on a test, then the weighted average is 143/150.  This is the way most every teacher (that I have had) averages grades.

Obviously, the average of a set of different fractions is between the lowest and highest fractions in the set.  However, this isn't necessarily true when the denominator is negative, because then it is weighted negatively in the average.


  Posted by Tristan on 2004-10-16 00:57:38
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information