Finding Fractions between FractionsDate: 01/08/2002 at 20:43:46 From: Kristen Subject: Fractions What are four fractions that are between 1/3 and 1/2? Date: 01/08/2002 at 21:42:46 From: Doctor Ian Subject: Re: Fractions Hi Kristen, If I have two numbers like 4 and 10, I can find a number right in the middle of them by adding the numbers and dividing the sum by 2: 4 + 10 14 ------ = -- = 7 2 2 It works with fractions, too! (In fact, it works with _any_ numbers.) So to find a fraction halfway between 1/3 and 1/2, 1/3 + 1/2 2/6 + 3/6 5/6 --------- = --------- = --- = 5/12 2 2 2 So now I have three fractions, in order: 1/3, 5/12, 1/2 I can do the same trick to find another fraction between 1/3 and 5/12, 1/3 + 5/12 4/12 + 5/12 9/12 ---------- = ----------- = ---- = 9/24 2 2 2 which gives me 1/3, 9/24, 5/12, 1/2 and another fraction between 5/12 and 1/2, or between 1/3 and 9/24, and so on, and so on. Now, this seems like a lot of work. Is there an easier way? Actually, there is. Note that I could have found 5/12 in this way: 1/3 < ? < 1/2 4/12 < ? < 6/12 It's pretty clear that 5/12 goes in the middle there. So what if I used an even bigger denominator? 1/3 < ? < 1/2 8/24 < ? < 12/24 Now you can get three fractions in there: 9/24, 10/24, 11/24. What would happen if you used 48 as a denominator? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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