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Working with Real Numbers

1. List all the sets in the real number system to which the given number

belongs.

(A) 15

(B)

(C) –π

(D) –100

(E)

2. Use interval notation to represent the indicated interval. State the interval

type.

(A) all numbers less than –4.5

(B) –12 ≤ x ≤ 28

(C)

(D) all negative numbers

(E) all real numbers

3. For each statement, tell which of the following properties of the real

numbers, R, with respect to the operations of addition and multiplication is

illustrated: Closure, Commutative, Associative, Additive Identity,

Multiplicative Identity, Additive Inverse, Multiplicative Inverse,

Distributive Property, Zero Factor Property.

(A) 0.45(2500) ∈ R

(B)

(C)

(D) ∈ R

(E) 23 (11 9) = (23 11) 9

(F) 50(10 4) = 500 200

(G) – = 0

(H) –99 · 0 · 100 = 0

(I)

(J)

4. Evaluate as indicated.

(A) | 20.9 |

(B)

(C) – | –80 |

(D)

(E) | a |, when a is negative

5. Insert , or = in the blank to make a true statement.

(A) – | –3 | ________ – | 2 |

(B)

(C) | –1.25 | ________ | 1.25 |

(D) – | –b | ________ | b |, b ≠ 0

(E) | – 15 | ________ | –30 |

For questions 6 to 15, compute as indicated.

6. –100 –50

7. 0.8 –1.9

8. –34 –(–22)

9.

10.

11. (–200)(–6)

12. –175.54 3.48 1.23

13. 125 – (–437) – 80 359

14. (–0.25)(–600)(4.5)(–50)

15.

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For questions 16 to 20, evaluate the given expression.

16. (–3)

4

17. –3

4

18. 49

19. 5

–3

20. 32

21. ( )

0

For questions 22 to 30, simplify the given expression. Assume that all variables

are positive.

22. x

5 x

3

23.

24. (z

3)

4

25.

26.

27. (a

3b

6)

28. (u

–2)

4 v

7 v

–9

29.

30.

For questions 31 to 40, simplify using the order of operations. Refer to the

following guidelines as needed.

Order of operations (PEMDAS):

1. Do computations inside Parentheses (or other grouping symbols).

2. Evaluate Exponential expressions (also, evaluate absolute value, square

root, and other root expressions).

3. Perform Multiplication and Division, in the order in which these operations

occur from left to right.

4. Perform Addition and Subtraction, in the order in which these operations

occur from left to right.

31. (7 8)20 – 10

32. (–9

2)(5 – 8)

33. (20 – (–30))

34. 8(–2) –

35.

36. (–2)

4 · –3 – (–15 – 4)

2

37. 3(–11 3 · 8 – 6 · 3)

2

38.

39.

40.

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Complex Numbers

For questions 41 to 55, perform the indicated computation.

41. (–8 –5i) (6 – 7i)

42. (9 4i) (5 – 4i)

43. (1–i ) (–7 2i )

44. (16 – 5i) – (–3 7i)

45.

46. (4 3i)(10–i)

47. (–2 – 5i)(4 – 8i)

48. (7 2i)(7 – 2i)

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