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Finite Mathematics JZM1 task 4.docx JZM1 â€“ Finite Mathematics Task 4: Ordering Par

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Finite Mathematics JZM1 task 4.docx JZM1 â€“ Finite Mathematics Task 4: Ordering Part A: Given that x and y are positive integers, explain why it is incorrect to claim that is always irrational First, we need to ...

Finite Mathematics JZM1 task 4.docx JZM1 â€“ Finite Mathematics Task 4: Ordering Part A: Given that x and y are positive integers, explain why it is incorrect to claim that is always irrational First, we need to understand what an irrational number is. By definition, an irrational number is a set of numbers whose decimal representations are neither terminating nor repeating (Blitzer, 2017). It is incorrect to claim that is always irrational for two reasons. One being that not all square roots are irrational. The second reason is that if âˆšy is a perfect square, then it is a rational number. For example, if x = 2 and y = 9 then the result is = which is a rational number because the decimal representation of is 0.666666 repeating which by definition, is a rational number. Part B: Given that 0 < A < B, explain why it is correct to claim that is true In this scenario, it is given that B will always be the larger of the numbers involved. This means that is what is known as a proper fraction because A, the numerator is smaller than (less than) B, the denominator. In the second set of , the numerator, B, is now larger (more than), the denominator, A, and is known as an improper fraction because it is equal to more than a whole number. For example, if we state that A = 10 and B = 15, then the original given statement would look like 0 < 10 < 15 and our fractional representation would be . This means that our first fraction is equal to less than one but the second fraction is equal to . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. .. . . . . . . . . . . . . . . . . . .. . . . .

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