Integers and Absolute Value

Definition: The term integer represents all natural numbers and their opposites. Fractions and decimals are not integers.

Integers can be shown as a set of numbers, as in this example:

Set of Integers



Or integers can be represented on a number line as in this example:

integers number line




If a number is greater than 0, it is called a positive integer. No sign is needed to indicate a positive integer.

Look at the number line above. All numbers to the right of 0 are positive.

Examples: 4, 8, and 15 are positive numbers.

The arrows on the end of the number line indicate that the number line goes on until infinity (forever).

Positive integers are pretty easy at this point, because you've been working with them since you started school!

So... let's move on.

For every positive integer there is a negative integer. They are called opposites.

Examples:

5 and -5 are opposites

20 and -20 are opposites




Negative Integers


Negative Integers are less than 0 (or to the left of 0 on the number line.) If a number is negative, there will be a negative (-) symbol in front of the number.

Example: -2, -6, and -20 are negative integers

The trickiest thing to understand about negative numbers is that the farther away from 0, the smaller the number.

Example: -5 is less than -2.

(Think about this - if you OWE someone $5, then you will have less money after paying, than if you only OWED $2.

Other Examples: -10 is less than -8.

Or... you could say that -3 is greater than -19.

TIP: Think of it this way- The closer the negative number is to being positive, the larger it is!




Absolute Value


Definition: Absolute Value is the value of the number without regards to its' sign. The value is ALWAYS a positive number!

The absolute value symbol is shown with the following symbol: |n| where n is any number.

Examples:

|7| = 7

|-5| = 5

|-10| = 10

TIP: Your answer is just the number within the absolute value sign. Do not bring the sign with it!


If you are following the Pre-Algebra Curriculum, then you are ready to move onto Comparing Integers.


If you are following the Algebra 1 Curriculum, then you are ready to move onto Adding Integers.



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