49. What is the estimated product when 157 and
817 are rounded to the nearest hundred and
multiplied?
a. 160,000
b. 180,000
c. 16,000
d. 80,000
50. (−12) + 4 =
a. zero
b. −4
c. −8
d. −16
51. 5 × (−7)
a. −12
b. 12
c. 35
d. −35
52. −4 + (−4) =
a. 16
b. −16
c. 8
d. −8
53. 6 + (−10)
a. 4
b. −4
c. 16
d. −16
54. 16 + (−16) =
a. zero
b. 32
c. −32
d. 16
55. Which of the following choices is equivalent to
6 × 6 × 6?
a. 3 × 6
b. 12 × 6
c. 63
d. 36
56. Which of the following choices is equivalent
to 25?
a. 7
b. 10
c. 16
d. 32
57. Which of the following represents a composite
number?
a. 11
b. 29
c. 41
d. 91
58. 172 =
a. 34
b. 68
c. 136
d. 289
59. 105 ÷ 102 =
a. 13
b. 103
c. 107
d. 1010
60. −42 =
a. −8
b. 8
c. −16
d. 16
61. −53 =
a. −15
b. 15
c. 125
d. −125
62. (−11)2 =
a. 121
b. −121
c. −22
d. 22
63. What is the square root of 36?
a. 2
b. 6
c. 18
d. 1,296
64. Which of these equations is INCORRECT?
a. 16 + 3 = 16+3
b. 6 ×12 = 6 ×12
c. neither is incorrect
d. both are incorrect
Answers:
49. a. 157 is rounded to 200 and 817 is rounded to
800; 200 × 800 = 160,000.
50. c. When adding negative numbers, follow this
rule: If both numbers have different signs,
subtract the smaller number from the larger.
The answer has the sign of the larger number.
Therefore, the above equation becomes: 12 −
(not +) 4 = 8. Since the larger number, 12, has
a negative sign, the answer has a negative sign,
so the answer is −8.
51. c. When multiplying integers (the set of whole
numbers and their opposites), begin by multiplying
the numbers together; 5 × 7 = 35. Then
if there is an even number of negatives in the
problem, the answer is positive. If there are an
odd number of negatives, the answer is negative.
In this question, there are two negative
signs, so the solution is 35.
52. d. When adding negative numbers, if both
numbers have the same sign, begin by simply
adding. If the sign of both numbers is negative,
the answer is negative.
53. b. You are adding numbers that have different
signs; therefore, subtract the smaller from the
larger: 10 − 6 = 4. Now give the answer the
same sign as the larger number, which in this
case is a negative number, so the answer is −4.
54. a. When adding two numbers that are the
same, if the two numbers have opposite signs,
the answer is zero.
55. c. The meaning of 63 is 6 to the power of 3, or 6
used as a factor 3 times; 6 × 6 × 6 = 63.
56. d. In this problem, 2 is the base and 5 is the
exponent. Two raised to the power of 5 means
use 2 as a factor five times; 2 × 2 × 2 × 2 ×
2 = 32.
57. d. A composite number is a whole number
greater than one that has other factors besides
1 and itself; in other words, it is not prime.
Each of the answer choices are prime numbers
except 91, which has factors of 1, 7, 13, and 91.
58. d. 172 means 17 squared and is equivalent to
17 × 17, which equals 289.
59. b. To solve this division problem, subtract the
exponents only: 5 − 2 = 3, so the answer is 103.
60. c. –42 means the opposite of the result of 4
raised to the second power. Think of it as –1 ×
42. As in order of operations, evaluate the
exponent first and then multiply; –1 × 16 =
–16.
61. d. –53 means the opposite of the result of 5
raised to the third power. Think of it as –1 ×
53. As in order of operations, evaluate the
exponent first and then multiply; –1 × (5 × 5 ×
5) = –1 × 125 = –125.
62. a. Since there are parentheses, the base in this
question is –11; (–11)2 means –11 × –11
which is equal to 121. Because there is an even
number of negatives, the answer is positive.
63. b. To find the square root of a number, ask
yourself, “What number times itself equals
36?” Six times itself, or 62 equals 36. Therefore,
the square root of 36 is 6.
64. a. Square roots can be multiplied and divided,
but they cannot be added or subtracted.
