The number - 13 can be classified as:

A) real and irrational

B) real and integer

C) real and natural

D) real and whole

Answer: Choice B) real and integer

Explanation:

The set of integers is { ..., - 3, - 2, - 1, 0, 1, 2, 3, ... } basically its the set of positive and negative whole numbers, including 0 as well. The set of whole numbers is {0, 1, 2, 3, 4, ... } so any positive number that does not a fractional or decimal part. The value 0 is included in the set of whole numbers. The natural numbers is {1, 2, 3, 4, ... } so it is the set of whole numbers but we kicked out 0 from this set. The set of natural numbers is also called the set of counting numbers.

If we take any two integers and divide them then you'll get a rational number. You cannot have zero in the denominator, but you can have any other integer. For example, 2 and 3 divide to get the fraction 2/3 which is a rational number. Numbers that we cannot express as a fraction of two integers are said to be irrational. An example of this is pi = 3.14 which is irrational. We cannot write pi as a ratio of two integers. One approximation is pi = 22/7, but this doesn't represent pi exactly. Any integer itself is rational. Something like - 13 can be written as - 13/1, so we cannot say - 13 is irrational. That rules out choice A. Choice C is ruled out because negative numbers aren't natural numbers. The same can be said about - 13 not being part of the whole number set {0, 1, 2, 3, 4, ... } so choice D is also false.