Basic Mathematics for College Students

Chapter 2 Summary and Review 195

To evaluate expressions that contain several
additions, we make repeated use of the rules for
adding two integers.

Evaluate:

Perform the additions working left to right.

 25

 26  1

 7  1 (20) 1  6 (20) 1

 7  1 (20) 1

We can use the commutative and associative
properties of addition to reorderand regroup
addends.

Another way to evaluate this expression is to add the negatives and

add the positives separately. Then add those results.

Negatives Positives

 25

 27  2

 7  1 (20) 1 [ 7 ( 20 )]( 1  1 )

If the sum of two numbers is 0, the numbers are
said to be additive inversesof each other.

3 and  3 are additive inversesbecause. 3 (3) 0

Addition property of opposites
The sum of an integer and its opposite (additive
inverse) is 0.

4 (4) 0 and 712 (712) 0

Addition property of 0
The sum of any integer and 0 is that integer.

 2  0  2 and 0 (25) 25

At certain times, the addition property of opposites
can be used to make addition of several integers
easier.

Evaluate:

Locate pairs of opposites and add them to get 0.

The sum of any integer

and 0 is that integer.

 8

14 (9) 8  9 (14) 0  0  8

14 (9) 8  9 (14)

Opposites

Opposites

 

 

Add.

13. 
    
    
    
    14. 
        
    
    
    
    


14. 
    
    
    
    16. 
        
    
    
    
    


15. 
    
    
    
    18. 
        
    
    
    
    


16. 
    
    
    
    20. 
        
    
    
    
    


17. 
    


18. 
    


19. 
    


20. 
    


21. 
    


22. 
    


23. 
    

    Find the sum of , 73, and.

    
    


24. 
    

    What is 3,187 more than?

    
    


25. 
    

    What is the additive inverse of each number?

    
    

a. b. 4

30. a. Is the sum of two positive integers always
    positive?

 11

 59

 102  345

 5 (31) 9  (9) 5

 2 (1)(76) 1  2

0 (20)

 4  0

( 2 11)[(5)4]

[7(9)]( 4 16)

 1 (4)(3) 3 (2)(4)

 8  8 73 (73)

 28  60 93 (20)

 6 (4)  3 (6)

b. Is the sum of two negative integers always

negative?

c. Is the sum of a positive integer and a negative

integer always positive?

d. Is the sum of a positive integer and a negative

integer always negative?

31. DROUGHT During a drought, the water level in a
    reservoir fell to a point 100 feet below normal. After
    a lot of rain in April it rose 16 feet, and after even
    more rain in May it rose another 18 feet.
    a. Express the water level of the reservoir before
    the rainy months as a signed number.
    b. What was the water level after the rain?


32. TEMPERATURE EXTREMES The world record
    for lowest temperature is. It was set on July
    21, 1983, in Antarctica. The world record for highest
    temperature is an amazing 265° F warmer. It was set
    on September 13, 1922, in Libya. Find the record
    high temperature. (Source:The World Almanac
    Book of Facts,2009)

129° F

REVIEW EXERCISES