Download Operations with Real Numbers

OPERATIONS WITH REAL NUMBERS
1) Write if each statement is true or false.
a) The absolute value of a number is never negative.
b) The opposite of a negative number is a positive number.
c) The numbers -35 and 35 can be referred to as additive inverses, as well as opposites.
d) In adding or subtracting numbers, if the two numbers are both negatives, then you add the
numbers and keep the common sign of a negative.
e) In adding or subtracting numbers, if the two numbers are both positive, then you add the
numbers and keep the common sign of a positive.
f) In adding or subtracting numbers, if one number is positive and the other number is negative,
then you subtract the numbers and keep the sign of the larger number.
g) To simplify the expression, |5 - 8|, the negative sign changes to a positive sign and then the
numbers are added; i.e. |5 + 8| = |13| = 13.
h) In multiplying or dividing numbers, if both numbers are positive, then your product or
quotient is a positive number.
i) In multiplying or dividing numbers, if both numbers are negative, then your product or
quotient is a positive number.
j) In multiplying or dividing numbers, if one number is positive and the other is negative, then
your product or quotient is a negative number.
k) The product of -21 and 21 is estimated to be about 400.
2) Fill in the blanks <, >, or = to make a true expression.
a) 0 _____ -5
b) 6 _____ -7
c) -5 _____ -8
d) -(-6) _____ 6
e) |-10| _____ -10
f) - |-8| _____ -8
g) -|6 - 2| _____ -(2 + 3)
h) -(-9) _____ -|-9|
3) Perform the indicated operations.
a) 10 - 5
f) 15 - (-25)
b) -10 + 5
c) 10 - (-5)
g) -27 + (-14)
d) 5 - 10
h) -50 - (-20)
e) -10 - 5
i) 47 - 14 - (-15)
j) 15 + (-18) – 3
4) Perform the indicated operations.
a) 8(-3)
b) -9(2)(-1)
f) -60 ÷ 0
c) 
48
6
d)
 125
5
e) (-6)(-6)(0)
g) 0 ÷ -6
Find each answer.
5) Carina has a balance of $186.42 in her checking account. Find her new balance if she writes
a check for $232.45.
6) Marv Levine bought 250 shares of Sunco stock for $21.50 per share. He sold it for $16.00
per share. Find the total amount of his loss and indicate it as a signed number.
7) In January 1991, Uptown Photo showed a loss of $726. In January 1994, they showed a
profit of $1935. What is the difference in these amounts?
8) The record low temperature in Cleveland for January 19 is -14 F and the record high on
July 19 is 103 F. What is the difference in these temperatures?
9) The Chicago Bears football team gained 2 yards on their first play, lost 9 yards on the
second play and lost 10 yards on their third play. What is the net gain or loss for the three plays?
10) The temperature at 6:00 am in Buffalo, NY was 16 F. By noon it had increase 15 and by
8:00 p.m. it had fallen 11. What was the temperature at 8:00 p.m.?
11) Frank DeMarco works in a chemical plant. The reading on a gauge when he starts his shift
at 6:00 am is –3.42. By 9:00 am the reading on the gauge is –14.75. How much did the reading
change (express as a signed number)?
12) Shariff travels 29 miles from his home in an easterly direction to get to his job. From there
he travels 41 miles due west to go to his evening class at Bloomfield College. How far must he
travel to get home after class?
13) -6 + 5
14) -5 + -6
15) -5 + 6
4 – 18
19) 8 – (-9)
20) 9(-2)(-1)
18)
22) 21 - |-10| + 3 – (-5) – 4
23)
25) (-6)(3) + (4)(-5)
26) 24 - 5(7 - 10)
28) (-5)(3) - (4)(-4)
29) 27 + 5(6 - 9)
16) -6(-5)
17)
21) -1 – 9 + (-8) – (-5)
|-10 + 5 - 20| - (-5)2
24) 52 + 2(-3)
27) 53 - 2(-3)
30) (-5 + 2  13)(8 – 12)
31) -132 ÷ 4 • 3 – 12 – (-14) • 5
32) 36 - 4[3 – 28 ÷ 7] – 30
33) 12 + 2(4 – 7)3
34)
35) -12 + 0.5 – 10
38)
(-9 ÷ 3) . 5 ∙ (-5 ÷ 2)
41) 2(-6 ÷ 3) -
2
45
(15 )
3
3
44) -6 ÷ (6 ÷ 7 . -2)
36) 8
  24 


 3 
 9[3  2(4)]
3(4  1)
3
+ 0.4
5
39) 3 - (4 ÷ 5 + 6)
42) -12 ∙ 4
2
1
45)  (10  4.2)  (8  5)
5
4
37) -5 – 1 ÷ 2
40) 0.2 + 5.08 – 0.36 + 5
43) 36 - 18∙ 2  -4
1
2
4  2.5
8
46)
 3
47)    
 8
2
6 7
48)    
7 6
2
 5
49) 

 10 
2
1
3  15 
51)    3   
9
 16 
 11
  1

 2     6
53)  
 36
  6

4 2 3 2
54)       
9 9 5 3
3
1
56)  4  2  - (-2 ÷ 6)
4
8
5
1 3 1
1
57)  13  1    2
8
4 8 2
8
4
2
1
 
 10 
3
0
 4 24   14 13 
50)        
 6 36   13 14 
1 1  2

58)           3  4 
3 9  3

3
2
1 5

52)   2    
2 2

2
2
55) (-5 ÷ 15) + (-3 ÷ 4 ∙ 2)