Chapter R Section 1

Work with Sets

“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”

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}

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

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

Example

Definition

Example Then what is the complement of A?

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?

Figure: Venn Diagrams as visual representations

Figure: Venn Diagrams as visual representations

Classify Numbers

 

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

Approximations 20.98 20.99

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

Evaluate Numerical Expressions

Order of Operations

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

Solutions worked out

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

Work with Properties of Real Numbers

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

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

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

Make sure you remember how to use these properties!

Make sure you remember how to use these properties!

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

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.

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

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

Watch those negatives!

Watch those negatives!

When can I “cancel?”

My favorite property!

How to work with fractions”

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

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