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Adding Integers and Subtracting Integers




 

In these lessons, we will look at adding integers and subtracting integers using the number line and using rules.

Related Topics:
More Lessons on Integers , Integer Worksheets, Integer Games

Using the Number Line

When we add, we move right on the number line.

When we subtract, we move left on the number line

Adding Integers

Example:

To evaluate –3 + 2 , we start at –3 and move 2 places to the right

The answer is –1

 

Subtracting integers

To evaluate –3 – 2 , we start at –3 and move 2 places to the left


The answer is –5




The following video will show an example of adding integers and subtracting integers using the number line.
How to think about adding and subtracting integers on a number line.


 

Using Rules to Add Integers

Using the number line to add or subtract integers may be quite tedious. A quicker method would be to use the following rules:

Rule 1 :

The sum of two or more positive integers is a positive integer.
The sum of two or more negative integers is a negative integer.

Example:

(+7) + (+ 4) = + 11
(– 8) + (– 9) = – 17

Rule 2 :

To find the sum of a positive and a negative integer:
Subtract the two numbers (ignore the signs) and then keep the sign of the larger integer.

(– 9) + (+ 7) = – 2
(– 3) + (+ 5) = + 2

Rule 3 :

The sum of an integer and its opposite is equal to zero

(– 9) + (+ 9) = 0
(– 3) + (+ 3) = 0

The following videos will show some examples of using the rules to add integers.


Using Rules to Subtract Integers

To subtract integers, we can rewrite the subtraction problem as an addition problem. Instead of subtracting, we add the opposite.

  • Subtracting a postive is the same as adding a negative.

3 − (4) = 3 + (−4)

  • Subtracting a negative is the same as adding a positive.

3 − (− 4) = 3 + 4

We then follow the rules for adding integers.

This video states the basic rules for subtracting integers and provides examples. Each subtraction problem is rewritten as an addition problem.

Subtracting Integers using Rules



Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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