1. Chapter R
Section 1

3. Work with Sets

5. “A is the set of x such that x is an integer less than 5”
A list of the elements
Read a special way…
“A is the set of x such that x is an integer less than 5”

6. Write the set in roster method:
Colors of the American flag
F= {Red, white and blue}
Write the set in set builder notation:
A = {M,O,N,K,E,Y}
A = {x/ x is a distinct letter of the word MONKEY}

7. Terminology of sets Well defined Not well defined
ex. the collection of great actors

8. Definition Intersection of sets union of sets All elements combined
between the sets
Elements in common

9. Example

10. Definition

11. Example
Then what is the complement of A?

12. Relationships of sets B is a proper subset of A
if and only if every element in
B is also in A, and there exists
at least one element in A that
is not in B.
Two sets are equal if they
have exactly the same elements
B A
Two sets are equivalent if
they have the same number
of elements
Are sets A and B equivalent?

13. Figure: Venn Diagrams as visual representations

14. Figure: Venn Diagrams as visual representations

15. Classify Numbers

17. Example (a) Natural numbers (b) integers (c) Rational numbers
(a) Natural numbers
(b) integers
(c) Rational
numbers
(d) Irrational
(e) Real numbers

18. Approximations
20.98
20.99

21. Examples
Watch the video below for some examples on how to translate words into
Algebraic expressions and equations

22. Evaluate Numerical Expressions

23. Order of Operations

25. Examples
Evaluate each expression on your own, then check your answers:
= 19
= 37
= 𝟕 𝟑𝟎
= 38

26. Solutions worked out

27. math frac on your calc
Do you know how to use this feature?

28. Work with Properties of Real Numbers

29. Properties of Equality
Suppose a, b, c are real numbers. Then,
You learned these in geometry!

30. Make sure you remember how to use these properties!
Works with addition and multiplication

31. Make sure you remember how to use these properties!
Works with addition and multiplication

32. Make sure you remember how to use these properties!

33. Make sure you remember how to use these properties!

34. Make sure you remember how to use these properties!
What is the additive inverse of 6?
What is the additive inverse of −𝟖

35. Make sure you remember how to use these properties!
The multiplicative inverse, , of a nonzero real number a is also referred to as the reciprocal of a.

36. Definitions Subtraction is just ADDING THE OPPOSITE!
Division is just MULTIPLYING BY THE RECIPROCAL!

37. It is ok to multiply by zero
It is NOT ok to divide by zero

38. Watch those negatives!

39. Watch those negatives!

40. When can I “cancel?”

41. My favorite property!

42. How to work with fractions”

43. Example Adding & Subtracting fractions with different denominators:
Don’t forget using a common
denominator will affect the terms
in the numerator as well
6 is the LCM
(least common multiple)
of 3 and 2

44. Examples continued Multiplying fractions: Dividing fractions:
Multiply across the top
Multiply across the bottom
Reduce if necessary
Dividing fractions:
Change to multiplication
and flip the divisor