Question

Question #97247

Answer 1

It is an Integer, a Rational number and a Real number.

Explanation:

First, lets simplify that fraction as much as possible. Since -12 divides evenly into 4, the number we want to evaluate is `-3`.

Now let's look at the definitions of the terms we want to evaluate `-3` against:

• Integer: Any number that is not partial. It can be positive or negative. Example: (..., -2, -1, 0, 1, 2, ...) not 1.25432, `pi`, etc.

• Whole: The Whole number set id defined as the "counting" numbers, so the non-negative integers. (0, 1, 2, 3, ...)

• Natural: This set has a problem in definition in that it sometimes includes 0 and sometimes it doesn't. It is defined either as "the set of positive integers" or "the set of non-negative integers". Since this question also includes Whole, I'll assume the definition here is the first one (positive) i.e. (1, 2, 3, ...)

• Rational: A Rational number is any number that can be expressed as a fraction. As the denominator of a fraction can also be 1, it includes all the Integers. Example: `21/1, 13/4, 1/410, etc`

• Irrational: An Irrational number is any that cannot be expressed by a fraction. They present as numbers that have an infinite number of non-repeating integers after the decimal, such as `pi` or `e` or `sqrt2`

• Real number: Any number that can be represented in a line. Fractions, Rational, Irrational, Whole, Natural and Integers are all part of the Real number set.

Now that we have our definitions we can compare `-3` to them and see if it fits.

It fits the definition for Integer, Rational and Real, but does not for Whole, Natural and Irrational.