Before we begin let's get something crystal clear!
Below we will be using negative cubes and positive cubes . The most important thing to remember is that one red cube (positive) and one blue cube (negative) make zero! WATCH !

 

 

 

 

Adding Integers

 

When adding integers with the same signs, you add their absolute value and keep the common sign.

(+6 ) + (+9) = +15

 

(- 6) + (- 9) = -15

 


 


 

 

When adding integers with different signs, you subract their absolute values and keep the sign of the larger number.

(-6 ) + (+9) = +3

 

(+6) + (-9) = - 3

 


 


 

 

When adding opposite integers their sum is ALWAYS zero!

(- 6 ) + (+6) = 0

 

(+9) + (- 9) = 0

 


 


 

 

When adding zero to any integer, their sum is ALWAYS that integer!

(- 6 ) + (0) = - 6

 

(0) + (- 9) = - 9

 



 


 

 

 

Subtracting Integers

 

There is only one thing to remember when you want to subtract integers!

ADD A LINE,CHANGE THE SIGN!

 

For Example

-6 - (- 9)


-6 - (- 9)
 
 
Add a line,

Change the sign to its opposite.

Then follow your addition rules!
-6 + (+ 9) = +3

 

Let's try another one!

 

-12 - (+ 19)


-12 - (+ 19)
 
 
Add a line,

Change the sign to its opposite

Then follow your addition rules!
-12+ (- 19) = -31

 

 

 

Multiplying & Dividing Integers

Before I introduce you to "Sad Chad" and "Smiley Kiley" take a look at what the facial expressions mean!

 

When you multiply two numbers that are positive (Kiley Smiley's eyes), you multiply the numbers like you always have.

Now, because she is smiling your answer is positive!

(+6) x (+9) = +54

When you multiply a positive and a negative number (Sad Chad's eyes), you multiply the numbers like you always have.

Now, because he is frowning your answer is negative!

(+6) x (-9) = - 54

When you multiply a negative and a positive negative number (Sad Chad's eyes), you multiply the numbers like you always have.

Now, because he is frowning your answer is negative!

(-6) x (+9) = - 54

When you multiply two numbers that are negative (Kiley Smiley's eyes), you multiply the numbers like you always have.

Now, because she is smiling your answer is positive.

(-6) x (-9) = +54

Now if you look closely at Kiley Smiley and Sad Chad's nose, they are made up of the letters M and D. That means that these same rules apply when you are MULTPLYING AND DIVIDING!

 

QUESTION: What happens when you have more than one or two negative or positive numbers?

ANSWER: Well, the positive numbers do not determine the sign of an answer. To find out what negatives do look below.

 

GENERAL RULE

If there is an odd number of negatives the answer is negative.

Example: (1) x (-1) x (-1) x (-1) = ?
Because there are three negatives the answer is negative!

So, (1) x (-1) x (-1) x (-1) = -1

 

 

If there is an even number of negatives the answer is positive.

Example: (1) x (-1) x (-1) x (-1) x (-1) = ?
Because there are four negatives the answer is positive!

So, (1) x (-1) x (-1) x (-1) = 1

 

CLICK NEXT TO TRY SOME ON YOUR OWN!

 

 

These pages were made through TeacherTECH, the teacher professional development component of GirlTECH, which is sponsored by the Center for Excellence and Equity in Education (CEEE) with support from the National Science Foundation through EOT-PACI, RGK Foundation, the Verizon Foundation, Rice University, and HiPerSoft.

Copyright © June 2002 by Asale Harris.