Integers

Integers

Review

What are integers?

• Integers include all Whole Numbers and their OPPOSITES

• Integers DO NOT include fractions, or decimals

What are opposites?

• numbers that are the same distance from zero on the number line in the opposite direction.

  
  

• Zero is neither positive or negative and does not have an opposite.

Multiple Choice

What is the opposite of -10?

• 0

• 10
  

•  $\frac{1}{10}$  

•  $\frac{10}{1}$  

You can do different math operations with integers.

Addition

Subtraction

Multiplication

Division

Adding Integers

• If the signs are the same, keep the sign & add. 

• If the signs are different, keep the sign of the larger # & subtract. 

• EXAMPLE #1:  $5\ +\ 3\ =\ 8$  

• EXAMPLE #2:   $-5\ +\ 3\ =\ -2$  

• In EXAMPLE #2, the signs of our numbers are different. 5 is the larger #. Since the rule is to keep the sign of the larger #, we will keep the negative sign and then subtract.

Multiple Choice

 $-9\ +\ 2$  

• -11

• -18

• -7

• 11

Multiple Choice

 $80\ +\ 57$  

• 23

• 137

• -23

• -137

Multiple Choice

 $-32\ +\ 48$  

• 16

• 80

• -16

• -80

Subtracting Integers

• KEEP, CHANGE, CHANGE!

  
  

• What do we Keep, Change, Change?

   KEEP the sign of the first number the same, change subtraction to addition, and change the sign of the second number ! 

• What happens after the Keep, Change, Change is complete?

   Use addition rules !  

Example:  $3\ -\ 5$  

Step 1: KEEP 3.
Step 2: CHANGE subtraction to addition. 
Step 3: CHANGE the 5 to a negative 5. 
Step 4: Add using the addition rule. 

 $3\ +\ \left(-5\right)$  <-- 5 is the larger number. Keep the negative sign. Then, subtract. 
 $3\ +\ \left(-5\right)=-2$  

Multiple Choice

Rewrite

 $2\ -\ \left(-5\right)$  

•  $2+5$  

•  $2+\left(-5\right)$  

•  $-2+5$  

•  $2-\left(-5\right)$  

Multiple Choice

 $3-\left(-7\right)$  

• -4

• 4

• -10

• 10

Multiple Choice

 $-18-7$  

• -25

• 11

• 25

• -11

Multiplying & Dividing Integers

• SAME signs -- POSITIVE answer
   Examples:
     $\frac{-10}{-2}=5$  

   $\left(-4\right)\left(-10\right)=40$  
  

• DIFFERENT signs -- NEGATIVE answer
   Examples: 

   $\left(-4\right)\left(10\right)=-40$ 
   $\frac{-10}{5}=-2$  

Multiple Choice

 $\frac{2}{2}$  

• 4

• 0

• 1

Multiple Choice

 $\left(-3\right)\left(-9\right)$  

• -12

• -6

• 27

• -27

Multiple Choice

 $\left(-9\right)\left(-6\right)\left(2\right)$  

• -13

• 17

• 108

• -108