My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 5th, 2013, 09:02 PM   #1
Senior Member
 
shunya's Avatar
 
Joined: Oct 2013
From: Far far away

Posts: 429
Thanks: 18

999 fractions

Question: Find 999 fractions between 1/3 and 1/2 such that the difference between pairs of numbers next to each other is the same. (Hint: Find convenient equivalent fractions for 1/3 and 1/2)

My attempt:
The difference 1/2 - 1/3 = 1/6. This difference has to be divided into 1000 parts to get 999 fractions which lie between 1/3 and 1/2.
so each "step" between required fractions = (1/6)/1000 = 1/6000
Therefore required list is 2001/6000, 2002/6000,..., 2998/6000, 2999/6000

Am I correct? Is there a another/simpler way to solve this problem?
Did I use the hint?? I am very confused...
shunya is online now  
 
November 5th, 2013, 09:41 PM   #2
Senior Member
 
Joined: Oct 2013
From: Sydney Australia

Posts: 126
Thanks: 0

Re: 999 fractions

It all looks good to me.
That is how I would have done it.
Melody2 is offline  
November 7th, 2013, 12:18 AM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 20,969
Thanks: 2222

There are other correct answers as well. Can you find one?
skipjack is offline  
November 17th, 2013, 07:56 PM   #4
Senior Member
 
shunya's Avatar
 
Joined: Oct 2013
From: Far far away

Posts: 429
Thanks: 18

Re: 999 fractions

To skipjack

I tried the method of finding equivalent fractions
(1/3)*(2/2) and (1/2)*(3/3) gives 2/6...3/6
Using factor 2/2 for the above we get 4/12 and 6/12. ONE fraction in between 5/12
Using factor 3/3 for the above we get 6/18 and 9/18. TWO fractions in between 7/18 and 8/18
So using 1000/1000, we get 2000/6000 to 3000/6000 with 999 fractions in between. This is the same answer I got using the other method as above

Reducing the "step" size increases the number of fractions and increasing the "step" size decreases the number of fractions

If there is another way to find the answer, I can't see it.
Thanks
shunya is online now  
November 17th, 2013, 10:32 PM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 20,969
Thanks: 2222

Re: 999 fractions

You correctly found what may well have been the expected answer. However, other answers are possible by giving a slightly different meaning to "numbers next to each other". The concept of "next" implies the numbers have been ordered, but it doesn't imply they have been put in ascending order.

Even without the above change of interpretation, other answers are possible.
The 999 fractions could, for example, be 5/12, 10/24, 15/36, ... , 4995/11988. As the question doesn't require the fractions to have different values, each pair could differ by zero. (The question doesn't explicitly state that the numbers 1/3 and 1/2 are included when determining which pairs are considered.)
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
999, fractions



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
LCD in Fractions mikeinitaly Elementary Math 2 December 21st, 2012 03:27 AM
Fractions MathematicallyObtuse Algebra 5 December 27th, 2010 09:33 AM
(4x-2)/2 * 3x/4 = ?? (Fractions) GrindingxxTeeth Algebra 1 January 4th, 2010 01:44 PM
Simplifying fractions with variables in fractions nova3421 Algebra 1 September 9th, 2009 10:03 AM
Different fractions mensamedlem Elementary Math 3 September 9th, 2008 05:18 PM





Copyright © 2019 My Math Forum. All rights reserved.