Integers and Rational Numbers

Positive and Negative Numbers, Opposites, and Absolute Value

What are positive numbers?

A positive number is a number greater than zero. On a number line, positive numbers are located to the right of zero (on a vertical number line, positive numbers are located above zero).

Positive numbers do not need a sign, but you

may see them written with a “+” in front of them.

What are negative numbers?

A negative number is a number less than zero. On a number line, negative numbers are located to the left of zero (or on a vertical number line, negative numbers are located below zero). A

negative number will have a “ - ” in front of it.

Ex: -9

Example of a number line showing positive and negative numbers

What About Zero?

Zero is neither positive nor negative.

What are Opposites?

Every negative number is paired with a positive number. The numbers in the pair are the same distance from zero but in opposite directions on a number line. These number pairs are called opposites.Ex: -3 and 3 are opposites

Opposites (cont.)

Can you name another pair of numbers that are opposites?

What are integers?

Whole numbers and their opposites have a special name—integers. Integers are “counting numbers” and their opposites.

Some examples of integers are:-4, -3, -2, -1, 0, 1, 2, 3, 4

Zero is an integer, but it is not positive nor negative.

Where do fractions fit in?

Fractions also have opposites. For example, ½ and -1/2 are opposites.

Positive and negative integers, as well as fractions, are called rational numbers.

Rational numbers are numbers that can be expressed as one integer divided by another integer.

What is Absolute Value?

Absolute value is the distance of a number from zero on a number line. A distance cannot be negative, so absolute value will always be a positive number. To show absolute value, a number will be written between two bars as shown below:

Absolute Value (cont.)

Opposites have the same absolute value. Can you name two numbers that have the same absolute value?