7th Grade Section
WME@Kimpton Middle

Positive and Negative Integers

Positive and Negative IntegersWe know integers are whole numbers. An integer can be positive, negative, or zero.

  • A positive integer, such as +28 (or simply 28), represents an increase. On the number line it means moving forward to the right.

  • A negative integer, such as −12 (negative 12) represents a decrease (the opposite of increase). On the number line it means moving backward to the left.

number line

The quantity 10 and −10 are the same amount, except one is an increase and
the other is a decrease. If you add them together, you get zero.

If you take a number, positive or negative, and remove its sign then you get the absolute value of that number. Thus, the absolute value of -17 and +17 is 17.

Please note that the symbols + and − serve double duty in mathematics. They are used as signs for positive and negative as well as operators for add and subtract.

Let's experiment with positive and negative integers to better understand them.

  1. Adding a positive number

    +7 + 5 =   
    
    -7 + 5 =   
    
    -3 + 5 =   
    
    -5 + 5 =   
    
  2. Adding a negative number--add a decrease

    +7 + (-4) =   
    
    -7 + (-4) =   
    
    +3 + (-4) =   
    
    -5 + (-4) =   
    
  3. Subtracting a positive number--remove the amount

    +7 - 5 =   
    
    -7 - 5 =   
    
    +5 - 5 =   
    
    +3 - 5 =   
    
  4. Subtracting a negative number--remove a decrease means increase

    +7 - (-3) =   
    
    -7 - (-3) =   
    
    +5 - (-3) =   
    
    -5 - (-3) =   
    

Absolute Values

DEFINITION: The absolute value of an integer is the whole number without the sign.

Thus, abs(19) is 19 and abs(-19) is 19. We also use the absolute value notation |-8| = 8.



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