Idiot\'s Guides Basic Math and Pre-Algebra

38 Part 1: The World of Numbers

MATH TRAP

Try to get in the habit of calling a number less than zero “negative” rather than

“minus.” The word “minus” signals subtraction, and not everything you do with

numbers less than zero is a subtraction. Talking about “negative 4” reminds you that

it’s the opposite of “positive 4.”

The Integers

We call the set of whole numbers and their opposites integers. The set of integers can be written

like this: {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}. The order in which the numbers are written conveys

their value. Any negative number is less than zero. The more you owe, the less you have, so -5

is less than -3. Just as the counting numbers, or positive numbers, go up forever without end, the

negative numbers go down forever.

DEFINITION

The integers are the set of numbers that include all the positive whole numbers and

their opposites, the negative whole numbers, and zero.

The Number Line

One way to visualize the integers is to place them on a number line. Usually the line is drawn

horizontally, but you could make a vertical number line if you chose. Zero is marked at a point on

the line, and then the line is broken into sections of equal length, to the left and the right of zero.

The positive numbers are placed on equally spaced marks to the right of 0, getting larger as you

move to the right. The negative numbers are placed on equally spaced marks to the left of 0,

with -1 at the first mark left of 0, then -2 at the next mark to the left, and then -3 and so on. The

arrows on the ends of the line remind you that the numbers keep going. (We’ll fill in the spaces

between the integers soon.)

When you compare two numbers, remember that the number to the left is the smaller one. The

number 5 is to the left of 9 on the number line, so 5 is less than 9, and you know that -8 is smaller

than -1 because -8 is to the left of -1 on the number line. Any negative number is smaller than

any positive number, and the negatives are to the left of zero and the positives are to the right.

-8-7 -6 -5 -4 -3 -2 -1 0 12345678