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 
