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Section 1.1

Section 1.1. Numbers and Their Properties. Write a set of numbers using roster or set–builder notation. A. OBJECTIVES. Write a rational number as a decimal. B. OBJECTIVES. Classify a number as natural, whole, integer, rational, irrational, or real. C. OBJECTIVES.

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Section 1.1

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  1. Section 1.1 Numbers and Their Properties

  2. Write a set of numbers using roster or set–builder notation. A OBJECTIVES

  3. Write a rational number as a decimal. B OBJECTIVES

  4. Classify a number as natural, whole, integer, rational, irrational, or real. C OBJECTIVES

  5. Find the additive inverse of a number. D OBJECTIVES

  6. Find the absolute value of a number. E OBJECTIVES

  7. Given two numbers, use the correct notation to indicate equality or which is larger. F OBJECTIVES

  8. DEFINITION NATURAL NUMBERS The set of numbers used for counting.

  9. DEFINITION WHOLE NUMBERS The set of natural numbers and zero.

  10. DEFINITION INTEGERS The set of whole numbers and their opposites(negatives).

  11. DEFINITION RATIONAL NUMBERS All numbers that can be written as the ratio of two integers.

  12. DEFINITION IRRATIONAL NUMBERS Numbers that cannot be written as ratios of two integers.

  13. DEFINITION REAL NUMBERS Numbers that are either rational or irrational:

  14. DEFINITION ADDITIVE INVERSE The additive inverse(opposite) of a is –a.

  15. DEFINITION ABSOLUTE VALUE The distance between a and 0 on the real-number line

  16. CAUTION The absolute value is always positive or zero.

  17. DEFINITION TRICHOTOMY LAW If given any two real numbers, only one of three things is true: a is equal to b, denoted by a = b, or a is less than b, denoted by a < b, or a is greater than b, denoted by a >b.

  18. Practice Test Chapter 1The Real NumbersSection 1.1A Exercise #1

  19. Use roster notation to list the natural numbers between 5 and 9. The set of natural numbers between 5 and 9 is {6, 7,8} Note 5 and 9 are not included

  20. Practice Test Chapter 1The Real NumbersSection 1.1B Exercise #2

  21. Practice Test Chapter 1The Real NumbersSection 1.1C Exercise #3

  22. Classify the given number by making a check mark () in the appropriate row(s). Natural number Whole number Integer Rational number Irrational number Real number             

  23. Practice Test Chapter 1The Real NumbersSection 1.1D Exercise #4

  24. Practice Test Chapter 1The Real NumbersSection 1.1E Exercise #5

  25. Find:

  26. Practice Test Chapter 1The Real Numbers1.1F Exercise #6

  27. Fill in the blank with <, >, or = to make the resulting statement true:

  28. Section 1.2 Operations and Properties of Real Numbers

  29. Add, subtract, multiply, and divide signed numbers. A OBJECTIVES

  30. Identify uses of the properties of the real numbers. B OBJECTIVES

  31. PROCEDURE TO ADD TWO NUMBERS WITH THE SAME SIGN: Add their absolute values and give the sum the common sign.

  32. PROCEDURE TO ADD TWO NUMBERS WITH DIFFERENT SIGNS: Find the absolute value. Subtract the smaller from the greater number. Use the sign of the number with the greater absolute value.

  33. DEFINITION ADDITIVE IDENTITY For any real number a:

  34. DEFINITION SUBTRACTION OF SIGNED NUMBERS If a and b are real numbers:

  35. DEFINITION ADDITIVE INVERSE For any real number a:

  36. PROCEDURE SIGNIFY MULTIPLICATION

  37. PROCEDURE MULTIPLYING NUMBERS WITH OPPOSITE SIGNS To multiply a positive number by a negative number, multiply their absolute values and make the product negative.

  38. DEFINITION SIGNS OF MULTIPLICATION PRODUCTS Same signs: Positive(+) Different signs: Negative(–)

  39. DEFINITION IDENTITY FOR MULTIPLICATION For any real number a:

  40. DEFINITION MULTIPLICATION OF FRACTIONS

  41. DEFINITION DIVISION OF REAL NUMBERS If a and b are real numbers and b is not zero:

  42. DEFINITION SIGNS OF A FRACTION For any real number a and nonzero real number b, there are two cases of signs:

  43. DEFINITION ZERO IN DIVISION For a ≠ 0:

  44. CAUTION

  45. DEFINITION MULTIPLICATIVE INVERSE (RECIPROCAL) Every nonzero real number a has a reciprocal such that:

  46. DEFINITION DIVISION OF FRACTIONS

  47. Practice Test Chapter 1The Real Numbers Section 1.2A Exercise #7

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