Integers are defined as the group of positive numbers, negative numbers, and zero.   

 Negative numbers are always shown with a  minus (-)  sign.  Positive numbers do not need to have a + sign.   Remember integers are represented by small slashes on the number lines, and do not include the fractional or decimal numbers in between the slashes.

When adding and subtracting integers, it is helpful to use a number line! Use the following rules to remember how it is done!

When  adding integers,  think number line!    

• The first number tells you where to start.
• The second number tells you which direction to move from that starting point.  If the second number is NEGATIVE, move to the left,  if the second number is POSITIVE, move to the right.

In the example -5 + 3 = , start on the number line at -5 and since 3 is positive, move to the right 3 spaces!

(-5) + 3 = (-2)  

Let's try one with a negative second number.
In the example -4 + (-2) = , start on the number line at -4 and since     (-2) is negative, move to the left 2 spaces!

(-4) + (-2) = (-6)

 Remember, subtraction and addition are just opposite operations.  So to subtract integers,  just add the opposite of the second number.

First let's review "opposites"!  An opposite of a number is the same distance from zero. Soooo, (-8) is an opposite number from +8 (or 8), and  5 is the opposite of (-5).

So when subtracting integers, simply add the opposite of the second number!

• The first number tells you where to start.

• Change the subtraction sign to addition, and find the opposite of the second number.

• Then follow the rules for addition of integers!  (The second number then tells you which direction to move from that starting point.  If the second number is NEGATIVE, move to the left,  if the second number is POSITIVE, move to the right.)

Let's do some examples:

6 - 4 =

6 + (-4) = 2

One more example!  (Subtracting a negative is like adding a positive).

(-4) - (-2) =

(-4) + 2 = (-2)

  Practice 1

Practice 2