Arup says: if a b is fully simplified, then b must be a prime number. Val says that if a b has b as a prime number, then the expression is fully simplified. Who is right? Or are both or neither of them right? Show/explain and FIX any wrong statements to be correct, with evidence.

If a/b is fully simplified, then we cannot reduce the fraction further. One example is 2/7 which has b = 7 being prime. So far Arup is correct; however, we could have 3/10 as another example of an irreducible fraction with b = 10 this time and it is not prime (10 = 2*5). This is one of infinitely many counter-examples to disprove Arup's claim.

Val's claim is not correct either. Let's make b some prime number. For example lets make b = 11. Double this value to get 2*11 = 22 and we'll make this the value of 'a'. So a = 22. Then note how a/b = 22/11 = 2/1. I've shown that if b = 11, then it is possible to have a/b equal to a fraction that hasn't been fully reduced. The prime requirement on b is not necessary. Instead, we must ensure that 'a' and 'b' together do not have any common factors, which is what leads to fraction reduction. For more information, look up the term "relatively prime" or "coprime".

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