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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.




 

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

How to add integers and subtract 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

How to use 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 positive 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.

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 calculator and problem solver 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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