Lesson 2-3

Example 1	Subtract a Positive Integer
Find each difference.
a.  4 – 9
     4 – 9 = 4 + (-9)	To subtract 9, add –9.
	  = -5		Simplify.

b.  –6 – 7
     -6 – 7 = -6 + (-7)	To subtract 7, add –7.
     	   = -13		Simplify.

Example 2	Subtract a Negative Integer
Find each difference.
a.  5 – (-2)
     5 – (-2) = 5 + 2	To subtract –2, add +2.
	      = 7

b.  –8 – (-3)
     -8 – (-3) = -8 + 3	To subtract –3, add +3.
	       = -5

Example 3	Subtract Integers to Solve Problems
BUSINESS	A company’s annual report states that the largest monthly profit for the year was $12,500 and the largest monthly loss was -$6,250.  Find the difference between the largest monthly profit and the largest monthly loss.

Explore	You know the largest monthly profit and the largest monthly loss.  You need to find the difference between them.

Plan	To find the difference, subtract the loss from the profit.

Solve	12,500 – (-6,250) = 12,500 + 6,250		To subtract –6,250, add +6,250.
			     = 18,750			Add 12,500 and 6,250.
	The difference in monthly profit and loss is $18,750.

Examine	The difference between +$12,500 and -$6,250 must be 12,500 + 6,250 or $18,750.  The answer appears to be reasonable.

Example 4	Evaluate Algebraic Expressions
a.  Evaluate m – (-3) if m = 8.
m – (-3) = 8 – (-3)		Write the expression.  Replace x with 8.
              = 8 + 3		To subtract –3, add its additive inverse, 3.
	        = 11		Add 8 and 3.

b.  Evaluate x + y – z if x = 11, y = -7, and z = -5.
x + y – z = 11 + (-7) – (-5)		Replace x with 11, y with –7, and z with –5.
	         = 4 – (-5)		Add 11 and –7.
	         = 4 + 5			To subtract –5, add 5.
	         = 9			Add 4 and 5.