How many fractions can we find between $1/3$ and $1/4$ ?

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How many fractions can we find between $1/3$ and $1/4$ ?

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Answer 1 · 2016-12-12T01:09:43

There are infinite number of fractions between $1/3$ and $1/4$ like $7/24$ and $2/7$ .

Explanation:

There are infinite fractions between any two fractions. Let the fractions be $a/b$ and $c/d$ .

Then picking up any two positive numbers $m$ and $n$ , the number $(m×a/b+n×c/d)/(m+n)$ always lies between $a/b$ and $c/d$ .

Further $(m×a+n×c)/(m×b+n×d)$ also lie between $a/b$ and $c/d$ .

For example choosing $m=1$ and $n=1$ , the number between $1/3$ and $1/4$ using first method is $(1/3+1/4)/(1+1)=7/24$ , which lies between $1/3$ and $1/4$ . Similarly using second method $(1+1)/(3+4)=2/7$ lies between $1/3$ and $1/4$ .

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How many fractions can we find between $1/3$ and $1/4$ ?

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