Basic Mathematics for College Students

Remember that any subtraction problem can be rewritten as an equivalent
addition. We just add the opposite of the number that is to be subtracted. Here are
four examples:

• 4  8  4 ( 8 ) 4


• 4 ( 8 ) 4  8  12


•  4  8  4 ( 8 ) 12


•  4 ( 8 ) 4  8  4

Any subtraction can be written as addition of

the opposite of the number to be subtracted.

2.3 Subtracting Integers 159

2 Evaluate expressions involving subtraction and addition.

Expressions can involve repeated subtraction or combinations of subtraction and
addition. To evaluate them, we use the order of operations rule discussed in Section 1.9.

EXAMPLE (^3) Evaluate:
StrategyThis expression involves two subtractions. We will write each
subtraction as addition of the opposite and then evaluate the expression using the
order of operations rule.
WHYIt is easy to make an error when subtracting signed numbers. We will
probably be more accurate if we write each subtraction as addition of the opposite.
SolutionWe apply the rule for subtraction twice and then perform the additions,
working from left to right. (We could also add the positives and the negatives
separately, and then add those results.)
Add the opposite of 2, which is 2. Add
the opposite of 10, which is 10.
Work from left to right. Add  1 2 using the rule
for adding integers that have different signs.
 9 Use the rule for adding integers that have different signs.

 1 (10)

 1 ( 2 ) 10  1  2 ( 10 )

 1 (2) 10

Self Check 3

Evaluate:

Now TryProblem 37

 3  5 (1)

EXAMPLE (^4) Evaluate:
StrategyWe will consider the subtraction within the parentheses first and rewrite
it as addition of the opposite.
WHYBy the order of operations rule, we must perform all calculations within
parentheses first.
Solution
Add the opposite of 24, which is
24. Since 24 must be written
within parentheses, we write
 2 (24) within brackets.
Within the brackets, add 2 and 24. Since
only one set of grouping symbols is
now needed, we can write the answer,
26, within parentheses.
Add the opposite of 26, which is 26.
Use the rule for adding integers that have
different signs.

 54

 80  26

 80 (26)

 80 ( 2  24 ) 80 [ 2 (24)]

 80 ( 2 24)

Self Check 4

Evaluate:

Now TryProblem 49

 72 ( 6 51)

∂

EXAMPLE (^5) Evaluate:
StrategyThis expression involves one addition and two subtractions. We will
write each subtraction as addition of the opposite and then evaluate the expression.

(6)(18) 4 (51)

Self Check 5

Evaluate:

Now TryProblem 55

(3)(16) 9 (28)

8

7

0

10

 26

54