Performing Operations on Integers

Natalie Odom Pough

Lee Kirkland McCall

Bobby Cunningham

  • South Carolina State Indicators

  • What Are Integers?

  • Opposites

  • Absolute Value

  • Adding Integers

  • Adding Integers with Different Signs

  • Subtracting Integers

  • Multiplying and Dividing Integers

  • Self-Check Quiz


South Carolina State Indicators

Indicator 7-2.8: Generate strategies to add, subtract, multiply,and divide integers.

Indicator 8-2.1:  Apply an algorithm to add, subtract, multiply and divide integers.

What Are Integers?

An integer is the set of all whole numbers and their opposites.

For example, here is a set of integers {... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...}.


Two numbers with the same absolute value but different signs are called opposites.  An integer and its opposite are also called additive inverses.



The opposite of 7 is -7.

The opposite of -0.123 is 0.123.

The opposite of -12 is 12.







The absolute value of a number is the distance the number is from zero.

For example, the absolute value of -4 is 4.  We denote that by writing | -4 | = 4.  -4 is 4 units from zero to its left.

More examples:

|5| = 5

|-100| = 100

Adding Integers With The Same Sign


If the integers have the same sign, then just add the absolute value of the integers and keep the sign.

More Integers With the Same Sign!




-3 + -5 = -8


  • Click on the characters below to get a better understanding of this problem.

Adding Integers With Different Signs.



When adding integers with different signs use the following steps:

1.  Find the absolute value of each integer.

2.  Find the difference between the absolute values.

3.  The difference is the answer and keep the sign of the largest absolute value.

Now You Try!

Put your answers at the bottom of the page. To check your answers click on the guys below!

Subtracting Integers

The first step in subtracting integers is to rewrite all double negatives. 

In this example:

 -1 - (-4) = ?

1.  Notice that there are two negative signs side by side between the 1 and the 4.

2.  Draw a circle around the two negative signs and turn them into a positive.

 3.  Now rewrite the equation keeping the sign of the first number and adding the second number.

5.  You now have an addition problem and you will apply the steps for adding integers.

 **Your teacher may have taught you to "Keep Change Change" when subtracting integers.  It is VERY important to know why you are using the "Keep Change Change" method. This page helps you understand the "Keep Change Change" process so that you are able to understand and explain it in mathematical terms.






Now You Try!

*Remember to follow the steps on the previous page!

Subtracting Integers

If there are no double negatives to change, subtracting integers involves simply rewriting the equation as an addition equation and using the rules of addition.  The following steps should be followed:

1.  Change the subtraction sign to an addition sign.

2.  Make the term on the left of the addition sign negative.

3.  Follow the steps for adding integers.


Solve the above equations.  The guys at the bottom of the page can tell you the correct answer.


*Note:  The results of subtracting and adding a negative integer are the same.  It is just a different way to rewrite the same thing!

Multiplying and Dividing Integers 

Rules for Multiplying and Dividing Integers

If both integers have the same sign (both positive or both negative), the product and the quotient will be positive.


If the integers have different signs (one is negative and one is positive), then the product or the quotient will be negative.


This "Love" and "Hate" chart may help you remember the rules for multiplying and dividing integers!

(This is very similar to the "Tic-Tac-Toe" board presented in class. Use either method to learn how to multiply and divide integers)

It is good (+) to love (+), and it is bad (-) to hate (-)!

If you love to love, that is good. (positive x positive = positive or positive / positive = positive)

If you love to hate, that is bad. ( positive x negative = negative or positive / negative = negative)

If you hate to love, that is bad. ( negative x positive = negative or negative / positive = negative)

If you hate to hate, that is good. (negative x negative = positive or negative / negative = positive)

Multiplying and Dividing Integers

Steps for multiplication and division of integers.

1.  Look at the signs and determine the sign of the product or quotient using the love/hate chart on the previouse page.

2.  Multiply or divide the absolute value of the integers.

3.  Add the appropriate sign.


Complete the above problems placing your answers in the space prvided at the bottom of the page.  Then,  check with the guys for the correct answers.

Power Problems

Problems involving exponents are another type of multiplication.  A power is made up of a base and an exponent.  The base is immediately to the left of the exponent.  The exponent tells us how many times to factor (or multiply by itself) the base. If the closing parenthesis is immediately to the left of the exponent, then everything in the parenthesis will need to be factored.  If the integer is immediately to the left, then only the integer is factored.  Look at the above examples.

Now you try!

Find the value of the above powers.  Put your answers in the space provided at the bottom of the page. Check with the guys for the correct answers!

Self-Check Quiz

Solve the problems above, placing your answers in the space provided at the bottom of the page.  Then, go to the next page to check your answers.  If any of your answers are incorrect, review the appropriate section of the book and try again.

Answer Key