Basic Mathematics for College Students

Chapter 2 Summary and Review 197

another 75 feet, they came upon a much larger find.

Use a signed number to represent the depth of the

second discovery.

54. RECORD TEMPERATURES The lowest and
    highest recorded temperatures for Alaska and
    Virginia are shown. For each state, find the range
    between the record high and low temperatures.

REVIEW EXERCISES

33. Fill in the blank: Subtracting an integer is the same
    as adding the of that integer.


34. Write each phrase using symbols.
    a. negative nine minus negative one.
    b. negative ten subtracted from negative six
    Subtract.


35. 
    
    
    
    36. 
        
    
    
    
    


36. 
    
    
    
    38. 
        
    
    
    
    


37. 
    
    
    
    40. 
        
    
    
    
    


38. 
    
    
    
    42. Evaluate each expression.
    
    
    
    


39. 
    
    
    
    44. 
        
    
    
    
    


40. 
    
    
    
    46. 
        
    
    
    
    


41. 
    
    
    
    48. 
        
    
    
    
    


42. 
    
    
    
    50. 
        
    
    
    
    


43. 
    


44. a. Subtract 27 from.
    b. Subtract from 27.
    Use signed numbers to solve each problem.


45. MINING Some miners discovered a small vein of
    gold at a depth of 150 feet. This encouraged them
    to continue their exploration. After descending

 50

 50

(5)(28) 2 (100)

 70 [(6)2] 89 [(2)12]

1 (27)  12 (610)

 9  7  12  5  6  33

12  2 (6)  16  9 (1)

0  37 0 (30)

 6  106  7  1

 4 (8)  8 (2)

5  8  9  12

Alaska Virginia

Low: Jan. 23, 1971 Low: Jan. 22, 1985

High: 100° June 27, 1915 High: 110° July 15, 1954

80° 30°

55. POLITICS On July 20, 2007, a CNN/Opinion
    Research poll had Barack Obama trailing Hillary
    Clinton in the South Carolina Democratic
    Presidential Primary race by 16 points. On January
    26, 2008, Obama finished 28 points ahead of Clinton
    in the actual primary. Find the point change in
    Barack Obama’s support.


56. OVERDRAFT FEES A student had a balance of
    $255 in her checking account. She wrote a check for
    rent for $300, and when it arrived at the bank she
    was charged an overdraft fee of $35. What is the new
    balance in her account?

SECTION 2.4 Multiplying Integers

Multiplying two integers that have different

(unlike) signs

To multiply a positive integer and a negative

integer, multiply their absolute values. Then make

the final answer negative.

Multiplying two integers that have the same

(like) signs

To multiply two integers that have the same sign,

multiply their absolute values. The final answer is

positive.

DEFINITIONS AND CONCEPTS EXAMPLES

Multiply:

Find the absolute values: and.

Multiply the absolute values, 6 and 8, to get 48.

Then make the final answer negative.

Multiply:

Find the absolute values: and.

Multiply the absolute values, 2 and 7, to get 14.

The final answer is positive.

2(7) 14

0  20  2 0  70  7

2(7)

6(8) 48

060  6 0  80  8

6(8)



To evaluate expressions that contain several

multiplications, we make repeated use of the rules

for multiplying two integers.

Another approach to evaluate expressions is to use

the commutative and/or associative properties of

multiplication to reorder and regroup the factors in

a helpful way.

Evaluate in two ways.

Perform the multiplications, working left to right.

First, multiply the pair of negative factors.

Multiply the negative factors to produce a

positive product.

 90

 5 (3)(6) 30 (3)

 90

5(3)(6) 15 (6)

5(3)(6)