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Quick Review

Now we have real numbers that include everything you find on a number line. We've got natural numbers that include all the numbers you would use when counting. We've also got whole numbers that include all of the natural numbers and zero. Does this mean we have explained all of the important numbers? No.

Going Negative

The first time you might find negative numbers is when you do subtraction problems. You can get to negative numbers when you count below zero. If you subtract more than you started with, you get negative numbers. Negative numbers may also be called the additive inverse of their positive values. For example, the additive inverse of 2 is -2. You may also hear that the opposite of 2 is -2.

3 - 5 = -2.
Is that -2 a real number? Yes
Is that -2 a natural number? No.
Is that -2 a whole number? No.

Integers

Okay, we know that all of the numbers on the number line are real numbers. How do mathematicians categorize the negative numbers? They have a group of numbers called integers. Integers include all of the whole numbers and their additive inverses (opposites). What? A simpler way of explaining it is to say that integers include all of the positive and negative versions of whole numbers.


2 is a whole number and an integer.
-2 is an integer, but not a whole number, because it is a negative value (less than zero).

589 is a real number, a natural number, a whole number, and an integer.
-589 is a real number and an integer. It is neither natural nor whole because it is a negative number.

1/41 is only a real number. It is not an integer because it is not a whole number. In the next section, you will learn that 1/41 is called a rational number.

Odds and Evens

Now that we know about integers, let's look at some different types. We have already talked about positive and negative integers. Imagine that you are a number for a moment. If you have a value less than zero, you would be called "negative". If you have a value greater than zero, you would be called "positive". If you chose to be the zero, you would be a very special number. Zero is neither negative nor positive.

Examples of negative numbers:
-2, -500, -5/16 (negative number, but not an integer), -3,000,567.
Look for the minus (-) sign in front of the number.

You will also learn about odd and even numbers. Even numbers can be divided by 2 with no remainder. 2 is an even number. 8 is an even number. 566 is an even number. They can all be nicely divided by 2. The other numbers are called odd. Odd numbers have a remainder of 1 when divided by 2. Another way to think of it is that odd numbers can never be divided into identical groups of two.

• 5 is odd (divide by two and have a remainder of one).
• 67 is odd (two groups of 33 with one left over).
• 1,587 is odd (two groups of 793 with one left over).

1 is also an odd number, because you can't make two groups at all. Just remember that one is an odd number. What about zero? It is even. When you divide zero by two, there is no remainder. Here's a good rule you can use...

• Even numbers end in 0, 2, 4, 6, and 8
• Odd numbers end in 1, 3, 5, 7, and 9

Negative numbers can also be odd or even and follow the same rules as positive numbers. 8 is even and -8 is even. 59 is odd and -59 is also odd.

Before We Go...

• Is -862 an integer? Yes. It is real, even, and an integer.
• Is 1/4 a natural number? No. It is a fraction, so it is only real. Fractions are not even or odd, since they are not whole numbers.

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