Download Practice Exam 3

Practice Exam 3
1. Reorder these numbers from smallest to largest:
2. Explain how one could use white (positive) and dark (negative) chips to model the
following:
A) 4 + (–6)
B) 5 – (–2)
3. Which properties does each of the following involve?
A) (–2 + 3) + –5 = (3 + –2) + –5
B) (–2 + 3) + –5 = –5 + (3 + –2)
C) (–2 + 3) + –5 = –2 +( 3 + –5)
4. Does 0 have a multiplicative inverse? Explain.
5. Complete the following:
A) – 7  – 8 =
B) 3  –5 =
E) 18 ÷ –3 =
F) –2 ÷ –5 =
I)
–
J)
 (– )
C) 16  –2 =
G) –18 ÷ 9 =
K) –8.6 ÷ 4.3
D) –21  –2=
H) 4 ÷ –16 =
L) –1.2 ÷ –2.4
6. Match the operations and the names of the properties by placing the correct number to the
left of the letters A–E. (Not all properties on the right will necessarily be used; some
may be used more than once.)
___A) –3  (2 + 5) = –3  (5 + 2)
___B) 3  (2 + 5) = (3  2) + (3 5)
___C) 4 + (–3 + –1) + 2 = (4 + –3) +( –1 + 2)
___D) 5 + ( 8 + 0) = 5 + 8
___E) -4  1 = -4
___F) 6 + (4 + –4) = 6 + 0
___G)
1.
2.
3.
4.
5.
6.
7.
___H) 3  (5 0) = (5  0)  3
___I) 3 + (2 + –5) = (3 + 2) + –5
8. Multiplicative identity property
9. Commutative property of multiplication
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Associative property of multiplication
Additive identity property
Multiplicative inverse property
Additive inverse property
Commutative property of addition
Associative property of addition
Distributive property of  over +
7. Consider clock arithmetic using a clock with four numbers: 0, 1, 2, and 3.
A) Complete these tables:
B) Do you think the set of numbers 0, 1, 2, 3, is closed under addition? If not, provide an
example that shows it is not.
C) Do you think the set of numbers 0, 1, 2, 3, is closed under multiplication? If not,
provide an example that shows it is not.
D) Is there an additive identity? If so, what is it?
E) Is there a multiplicative identity? If so, what is it?
F) Does 3 have an additive inverse? If so, what is it?
G) Does 2 have a multiplicative inverse? If so, what is it?
H) Do you think addition is commutative? If so, provide an example.
I) Do you think multiplication is commutative? If so, provide an example.
J) Do you think addition is associative? If so, provide an example.
K) Do you think multiplication is associative? If so, provide an example.
L) Do you think multiplication is distributive over addition? If so, provide an example.
8. 5 is a multiple of 0. Explain if false.
A) True
B) False
9. Circle T if the statement is true, F if it is false.
T F Every whole number is a multiple of itself.
T F It is possible for an even number to have an odd factor.
T F Zero is a multiple of every whole number.
T F 250 is a factor of 10030.
10. Does 0 have any factors? Explain your answer.
11. Of what numbers, if any, is 0 a multiple? Explain your answer.
12. Determine whether m and n are primes. Write only enough to make your decisions clear.
A) m = 23  29 (= 667)
B) n = 133
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13. Is 245 a prime number? Explain.
14. Is there a whole number M that would make this true? If so, tell what M is. If not, tell
why not.
A) 35 . 52 . 173 = 34 . 174 . M
B) 24 . 72 . 118 . 22 = 25 . 7 . 116 . M
15. Give the prime factorization of n, where n = 4  720  5000. If it is not possible, explain
why not.
16. It is correct that 3721164 = 12  172  29  37.
Give the prime factorization of 372116400 (notice the extra two zeros).
17. Fill in the blanks to make a true sentence. If no number or algebraic expression will
make the sentence true, say so.
A) An example of a number which has an odd number of factors is ____.
B) If n = 138 . 1710, then the prime factorization of 26 . n is ______________.
C) 3 will be a factor of 140000000?000000014 if the missing digit, ?, is __ or __ or __.
18. Tell the difference between (a) “give a prime factor of 350” versus “give a prime
factorization of 350” and the difference between (b) “give a number that has an odd
factor” versus “give a number that has an odd number of factors.”
19. In each part, find a whole number for m to make the equality true. If it is not possible,
explain why. For credit, your work should show an understanding of number theory.
A) 52  103 176 = 23 176  m
B) 52 76  114 = 5  356  114  m
20. Name the number of factors of each of these numbers and list them, in factored form.
b. 35
a. 52  173
21. For each part, give an example, if one exists. If there is no example, explain why not.
A) A whole number which has 15, 21, and 1000 as factors, but does not have 9 as a factor.
B) A prime number that has 7 and 19 as factors, and is not a perfect square.
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22. Write the prime factorization of each of the following. (Show your work.)
A) 1485:
B) 792:
C) Name all common factors of 1485 and 792 (They can be in factored form).
D) What is the greatest common prime factor of 1485 and 792?
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23. Suppose K = 25  7 11 , L = 23  7 1113
M = 2  29
and N = 4 1113  29
Name the least common multiple of each of the following (in factored form).
A) K and L
B) M and N
C) K and M
D) K, L, and N
24. Hamburger patties come in packages of 16, and hamburger buns come in bags of 12. How
many of each do you need to buy so that you have the same number of buns as you do of
hamburgers?
25. The band has been invited to march at the Rose Parade and need to make money to cover
the expenses. They divide up into three teams and shovel snow from long driveways for
four days before Christmas. The first team made $315, the second $240, and the third
$210. If they charged the same whole-dollar rate for each driveway, what was that rate?
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