Addition and Subtraction of Integers

by

Bernadette Dvorscak


Objectives:  

This lesson is designed for Sixth and Seventh Graders

Addition of Integers

When integers have the same sign, add the integers.  The sum will have the same sign as the integers.

        + 7 +  +8 = +15                      -9 +  -4 = -13

When integers have different signs,  find the difference between the two numbers.  The sum will have the sign of the integer with the largest absolute value.

        +8 + -5 = +3                         +4 + -9 = -5

Why?  Think of the integers as either negative or positive charges.  A positive and negative will bond and create a zero pair (additive inverse).  

Consider the problem  +3 + (- 5).

Blue counters represent positive integers.  Red counters represent negative integers

  Step 1:  Start with three positive counters.

                                                    

                         Step 2:   Five negative counters are added to the three positive counters.

Step 3:  The three negative counters combine with three of the positive counters to create zero pairs.  There value is zero.  There are two negative counters left.  Therefore, + 3 + (-5) = -2 

Worksheet 1

Find the sums of the following integers.

Addition Problem

Sum

     -7 + (+12)  
     8 + (-5)  
     -17 + 12  
     9 + (-14)  

    8 + (-5)

 

-16 + 16

 

-24 + 15

 

6 + (-13) + 16

 

-12 + 7 + (-5)

 
14 + (-27) + (-13) + 8  

Go to answers for Worksheet 1

Click HERE for more information and practice on adding integers.

Subtraction of Integers

When subtracting integers, the additive inverse must be used. The additive inverse of +8 is -8  (-8 + 8 = 0). 

-6 - (+8) = -6 + (-8) = -14

Why has the subtraction problem become an addition problem? 

Step 1:  Subtract +8  from -6 .   Start with eight negative counter.  

Problem!  There are no positive counters to subtract.

Solution!

Step 2:  Add 8 zero pairs ( -8 + 8 ).  Now  eight positive counters may be subtracted.  When +8 is subtracted, how many counters remain?

Step 3:  There are 14 negative counters left.

-6 - (+8) = -6 + (-8) = -14

Try this problem:  6 - 9 = n   All through school, you've been taught that you cannot subtract a large number from a smaller number. (Your second grade teacher probably made a big red check on your paper if you wrote a problem like this, 6 - 9.)   If you use integers, it is possible to do this subtraction problem.

Step 1: Start with six positive counters.

Step 2: Add nine zero pairs (-9 +9). 

Step 3:  Remove nine positive counters. Six zero pairs remain; their value is zero.  Three negative counters also remain.                                             Therefore:  6 - 9 = 6 + [9 + (-9)] = 6 + (-9) = -3

Worksheet 2

Find the difference of the following integers.

Subtraction Problem

Difference

     -9 - (+12)

 
     15 - (-7)  
     -8 - (+6)  
    -14 - (+9)  

   -5 - (+8)

 

-13 - (+13)

 

32 - (-12)

 

-27 - (+17)

 

21 - (+5)

 
-10 - (+11)  

 Click HERE for more information and practice on addition and subtraction of integers click


Project 1. 

In this project, you will record the changes in the price of stocks for for ten days.  Go to http://quotes.nasdaq.com/quote.dll?page=nasdaq100.  Select a company from the Nasdaq 100 list.  Record the symbol for the company and the closing price for the first day in the table.  Each day record the change in price as either positive or negative rational numbers.  Write an addition expression using the price changes and solve. 

Company name:

Date

Opening price

Change Addition expression Closing Price
Ex:11-29 $13.16 $.74 $13.16 + .74 $13.90
         
         
         
         
         
         
         
         
         
         

 

Date

Addition expression and value

   
   
   
   
   
   
   
   
   
   

Example:11-29

 12 + (-.15) + .17 + .12 + (-.18) + (-.11) + .14 = $11.99

 


Back to the SMART index page