Integers
Integers are the set of whole numbers and their opposites. The number line is used to represent integers. This is shown below.




  • The number line goes on forever in both directions. This is indicated by the arrows.
  • Whole numbers greater than zero are called positive integers. These numbers are to the right of zero on the number line.
  • Whole numbers less than zero are called negative integers. These numbers are to the left of zero on the number line.
  • The integer zero is neutral. It is neither positive nor negative.
Absolute Value
PENSANDO_EN_NUMEROS.jpg


The absolute value of an integer is its distance from zero on the number line. The absolute value of +3 is 3, and the absolute value of -3 is 3. Thus, opposite integers have the same absolute value. Mathematicians use the symbol || for absolute value.
Compare and Order Integers
When comparing two integers, we use the symbols < and >.
1 < 5
means 1 is less than 5

  • || -7 < -5 || means -7 is less than -5 ||
  • || +9 > -6 || means +9 is greater than -6 ||


Integer Addition
Rule: The sum of two negative integers is a negative integer.

Rule: The sum of two positive integers is a positive integer.

Rule: To add a positive and a negative integer (or a negative and a positive integer), follow these steps:

  1. Find the absolute value of each integer.
  2. Subtract the smaller number from the larger number you get in Step 1.
  3. The result from Step 2 takes the sign of the integer with the greater absolute value

Rule: The sum of any integer and its opposite is equal to zero.

Integer Subtraction
Rule: To subtract an integer, add its opposite.

Example :
+5 - +2

Step 1:
The opposite of +2 is -2.
Step 2:
Subtraction becomes addition.
Solution:
+5 - +2 = +5 + -2 = +3
integers.gif
Integer Multiplication
Rule 1: The product of a positive integer and a negative integer is a negative integer.Rule 2: The product of two negative integ

ers or two positive integers is a positive integer.
Example :
Find the product of each pair of integers.



Multiplying Integers
Integers
Product
Rule Used
(+7) (+3) =
+21
Rule 2
(+7) (-3) =
-21
Rule 1
(-7) (+3) =
-21
Rule 1
(-7) (-3) =
+21
Rule 2




Integer Division
Rule 1:
The quotient of a positive integer and a negative integer is a negative integer.
Rule 2:
The quotient of two negative integers or two positive integers is a positive integer.
Example :Find the quotient of each pair of integers.

Dividing Integers
Integers
Quotient
Rule Used
+24 ÷ +12 =
+2
Rule 2
+24 ÷ -12 =
-2
Rule 1
-24 ÷ +12 =
-2
Rule 1
-24 ÷ -12 =
+2
Rule 2
Practice Exercises: Integers

Order of Operations - PEMDAS




external image pemdas.gif

After you have done "P" and "E", just go from left to right doing any "M" or "D" as you find them.
Then go from left to right doing any "A" or "S" as you find them.
external image thought-sm.gif
You can remember by saying "Please Excuse My Dear Aunt Sally".
Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract), and in Canada they say BEDMAS (Brackets,Exponents,Divide,Multiply,Add,Subtract). It all means the same thing! It doesn't really matter how you remember it, just so long as you get it right.

pemdas-300x230.jpg