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Subtraction with Negative Numbers

1. Definition of subtraction: If a and b are any two numbers, then it is true that:

a - b = a + ( -b )

Note: Subtracting a number is the same as adding its opposite.

Ex: Write each of the given subtraction problems as an equivalent addition problem using the definition of subtraction.

a. 14 - 7 = 14 + (-7 )

b. 9 - 4

c. -13 - 5

2. Subtraction with negative numbers:

To subtract two numbers, rewrite the expression as "addition of the opposite", and then apply the addition rules.

Ex: Simplify:

a.

7 - (-5 )    
   = 7 + 5 change subtraction to addition of the opposite
   = 12 apply rule for adding numbers that have the same sign

b.

 

(-8) - (-5 )    
   = (-8) + 5 change subtraction to addition of the opposite
   = -3 apply rule for adding numbers that have the same sign

 

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