Exponents and Order of Operations

1
Exponents and Order of Operations
2
Exponents

• The exponent (little number) indicates how many
  times the base (big number) appears as a factor.

3
Order of Operationsp. 66 and 102

• Parentheses (grouping symbols)
• Exponents
• Multiplication/Division
• Working from left to right in order they appear.
• Add/Subtract
• Working from left to right in order they appear.

4
Arithmetic Mean

• Fancy way of talking about averages.
• Mean means average
• To average
• add up all the scores and divide by the number of
  scores.

5

• Questions???

6
A Return to Algebraic Expressions

• Term The number/letter combinations separated
  by addition signs in an algebraic expression.
• In my words
• The stuff being added together
• Example
• 3x 5y 7 terms are 3x, 5y, and 7

7
Components of an Algebraic Expression

• Constant term fancy name for a number
• Variable term terms with letters
• Example 3xy 4z 17
• Variable expression with 3 terms 3xy, -4z, 17
• 2 variable terms and 1 constant term

8
Variable Terms

• Consist of two parts
• The variable(letter) part
• The number part
• Example
• 2xy has a coefficient of 2
• -6j has a coefficient of 6
• W has a coefficient of 1

9
Algebraic Expressions

• Evaluating Algebraic Expressions
• Substitute a given value in for the variable and
  use order of operations to simplify

10
Translating Verbal Expressions into Variable
Expressions

• Recognize verbal phrases that translate into
  mathematical operations- see chart on page 76.

11
Example of evaluating an expression.

• Evaluate 3xy 2x 7y when x 2 and y 3
• 3(2)(3) 2(2) 7(3)
• 18 4 21
• 14 21
• 35
• The value of the expression is 35.

12

• Questions????

13
Terms

• Like terms
• Terms with the same variable part
• Same means same letter(s) and power(s)
• We simplify variable expressions by combining
  like terms.
• To combine like terms, work with the coefficients
  of the like terms

14
Combining Like Terms

• 3x 5 9x
• 6x 5
• -5 3b 7 5b
• -5 7 -12
• 3b 5b -2b
• Answer -2b 12

15
Simplifying Numerical Expressions

• Use order of operations.
• Simplifies to a single number
• See Chapter 1 pretest 1, 2, and 3
• Could also be referred to as evaluating

16
Simplifying Algebraic Expressions

• Rewrite using as few symbols as possible
• Use the distributive property if necessary to
  remove parentheses.
• Combine like terms
• More often than not will have numbers and letters
  in the final answer.

17
Opposite of an expression

• -(4a 3b 7c)
• Change everything on the inside to its opposite
• -4a 3b 7c

18
Distributive Property

• Distributive Property
• This property will be used on a continuous basis
  throughout this course.
• a(b c) ab ac
• Examples
• 2(30 5) 2(30) 2(5) 60 10 70
• 3(x 4) 3(x) (3)(4) 3x 12
• Taking the opposite can be considered
  distributing -1
• -(4a 3b 7c) -1(4a 3b 7c)

19
Simplifying using the distributive property

• 5x 9 3(2x 4)
• 5x 9 (3)(2x) 3(4)
• 5x 9 6x 12
• 5x 6x 11x
• -9 12 3
• Answer 11x 3

20
Distributing a negative

• -4(y 2) (-4)(y) (-4)(2)
• -4y (-8)
• -4y 8

21
Using the Distributive Property to Simplify

• 9t 5r 2(3r 6t)
• 9t 5r 6r 12t
• 9t 12t -3t
• -5r 6r -11r
• Answer -11r 3t

22

• Questions???