Task 4
Finite Mathematics Task 4:
Ordering
Given the following: Let x and y be positive integers when completing part A.
A. Explain why it is incorrect to claim that x
√
y
is always irrational.
It is incorrect to claim that x
√
y
is always irrational because y may be a perfect square
which would make the denominator an integer, or a rational number. An irrational number is one
that the numbers after the decimal do not repeat or terminate. If a perfect square is a number that
is the square of a whole number, then not all square roots will be irrational because the square
root of a perfect square is a whole number. A whole number has a decimal that terminates, which
would make it a rational number. So, if x∧ y are both positive integers, and y is a perfect
square then the number would be rational.
Given: 0 <A <B, complete part B.
B. Explain why it is correct to claim that AB
is true.
It is correct to claim that A<B
B <A
is true, because Bwould always be larger than a
B A A
whole and A
Bwould always be a fraction of a whole. If A <B, then the fraction A
Bwill
always be less than the fraction B . In the fraction A , A would be a part of the whole B,
A B
and when the fraction is inverted to B , then it would become an improper fraction.
A
