Question

two fractions 1/3 and 2/3 are given to you. Can you find a fraction that lies one third on the way between them?

Answer 1

Answer:

x=¹/₃︎ and y=²/₃︎

(n/3 + 2m/3)/(n+m)

(n+2m)/3(n+m)

n=m=1 is the simplest case

now besides that you can let n & m be any positive coprime integers, the coprime (meaning they have GCD of 1) ensures you don’t get repeated solutions.

For example:

n=2 and m=4 is the same result as n=1 and m=2,

because we can factor a 2 out of the entire numerator and entire denominator of the expression since 2 divides both n and m.

That’s why you want them coprime, to guarantee unique solutions as long as you don’t repeat pairs for n and m.

Answer 2

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