How many fractions can we find between \frac{1}{3} \text{and}\ \frac{1}{4}?

Jacob Stein

Jacob Stein

Answered question

2022-02-09

How many fractions can we find between 13and 14?

Answer & Explanation

Brom76g

Brom76g

Beginner2022-02-10Added 6 answers

Answer: 
There are countless possible fractions between 13and 14like 724and 27
Explanation: 
Between any two fractions, there are infinitely many fractions. Let the fractions be aband cd
Then picking up any two positive numbers m and n, the number m×ab+n×cdm+n always lies between aband cd
Further m×a+n×cm×b+n×d also lie between aband cd
For example choosing m=1and n=1, the number between 13and 14 using first method is 13+141+1=724, which lies between 13and 14. Likewise, using the second approach 1+13+4=27 lies between 13and 14.

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