Chapter 1 Section 2

1
Chapter 1 Section 2

• Real Numbers

2
Real Numbers

• Real numbers are numbers that can be graphed on
  the number line. (There ARE imaginary numbers,
  but well cover them later.)
• There are two basic types of real numbers
• rational and irrational numbers.

3
Rational vs. Irrational

• Rational numbers can be written as a ratio of
  one number to another, i.e. as a fraction. Most
  of the numbers you know are rational numbers.
  E.g., 13.5, ?, -17, 4, and any repeating decimal,
  like 3.888
• Irrational numbers cannot be written in this way,
  and so we give them names, like the square root
  of any number that is not a perfect square,
  pi, or e. Any number that goes on forever but
  does not repeat is irrational, e.g.
  0.101001000100001

4
The Real Number Venn Diagram

• Rational(Q) Irrational(I)
• Integer(Z)
• Whole(W)
• Natural(N)

5
A short lesson on repeating decimals

• Repeating decimals are rational numbers, and can
  be written as such by recognizing the following
  pattern
• So how would one write 4.127127127 as a rational
  number?
• And what does 3.99999 equal? (THINK!)

6
Properties of Real Numbers

• For all real numbers, the following are true
• Property Addition Multiplication
• Commutative a b b a a b b a
• Associative a (b c) (a b) c a (b
  c) (a b) c
• Identity a 0 a a 1 a
• Inverse a (-a) 0 a (1/a) 1
• Distributive a (b c) ab ac

7
Name the property

• (-8 8) 15 0 15 (answer?)
• Answer additive inverse property
• 5(8 - 6) 5 8 - 5 6 (answer?)
• Answer distributive property

8
Identify the inverses

• What is the additive and multiplicative inverse
  of
• -7 additive? multiplicative? (answer??)
• Answer additive inverse, 7
• multiplicative inverse, -1/7

9
More inverses (tricky!)

• What are the additive and multiplicative inverses
  of
• (answers??)
• Answers additive inverse, -1/3
• multiplicative inverse, 3

10
Use the Distributive Property

• If envelopes cost 0.13 and stamps 0.41 what are
  two ways to write the cost of buying 7 envelopes
  and 7 stamps?
• 70.13 70.41 and 7(0.13 0.41)
• Simplify 4(3a - b) 2(b 3a)
• 18a - 2b

11
Your assignent

• Chapter 1 section 2, 19-39 and 43-61 and 79-85
  odd, PLUS 26, 38, 48, 56 and 58.
• No man can sit down and withhold his hands from
  warfare against wrong and get peace from his
  acquiescence.
• --Woodrow Wilson