Solve the below question.

Let a and b be in the set of Natural Numbers. More formally, a b∈N

Select a few random values for a and b, and keep the numbers small.  Try to answer the following questions, ensuring that your answer is also a counting number!  Where does this break?  Which kind of operator causes a problem? Does the order of a and b matter? Check your answers with a calculator.  

 a+b=

 a −b=

ab=

ab=

Try that again, only this time your answer on the right hand side of the = must 15,16 or 17.  What do you notice about these numbers?  How many solutions do you have for each answer?  Loads or just one?  Does it matter if the answer is odd, even or a prime number?  Try some other numbers, odd, even and prime.  Can you see a pattern emerging?