Ch 1 – Introduction to Algebraic Expressions

1
Ch 1 Introduction to Algebraic Expressions

• 1.1 Introduction to Algebra

2
Algebra

• Difference between arithmetic and algebra?
• Specific vs General
• Paycheck
• 8.29/hr x 6.5 hr 53.885
• 8.29n

3
Algebra - Operations

• Math symbols are the same for both arithmetic and
  algebra
• , -, ?, powers, roots
• except multiplication

4
Algebraic Expressions

• Arrangements of numbers and letters and math
  operations used to represent a situation.

5
Writing Algebraic Expressions

• 1/8 of a workers salary goes into a mutual fund.

6
Writing Algebraic Expressions

• 17 more DUI arrests than in Crawford County.

7
Writing Algebraic Expressions

• By the end of the day, my stock portfolio dropped
  235.

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Writing Algebraic Expressions

• A winning lottery ticket earnings split three
  ways.

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Words that Signal Operations

• Brainstorm!
• Words that signal addition
• ____________________________________
• Words that signal subtraction
• ____________________________________

10
Words that Signal Operations

• Brainstorm!
• Words that signal multiplication
• ____________________________________
• Words that signal division
• ____________________________________

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Practice Writing Expressions

• Team up and do problems 31 54 on page 10.

31 - 38 r 5 4a b 6 7 L c 9 d 4 6
q 11 z
39 46 9p d c y x L 2 x/w x/y n m q - p
47 - 54 L h d f 9(2m) p 2w ¼(x) 1/3(x
y) .64x .38y
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Evaluate Algebraic Expressions

• Evaluate means
• figure out, compute,

Evaluate 9x 15 when x 8
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Evaluate Each Expression

• 21)
• When the number of hours worked gt 40 hrs, use
  this formula to determine pay.
• Determine the paycheck for an employee who is pay
  is r 8.95/hr and n4.5 hrs

14
Practice Evaluating Expressions

• Team up once again and work on 14-24 even on p.
  9, then do 26, 29, 30.

• 14 24 even
• 14) 3
• 16) 10
• 4
• 6
• 3
• 24) 3

• 24 hrs
• .368 average
• 45 sq cm

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Equations

• Expression
• Equation

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Verification

• You can check to see if an equation is true or
  not
• 14 x 3 42
• 21 3.1 18.9
• x 6 13

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Solutions to Equations

• A number that makes an equation true is a
  solution to an equation

7
x 6 13
7 6 13
13 13
? 7 is a solution to the equation.
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Writing Equations to Represent a Situation

• What number plus 47 is 89?

x

47

89
19
Writing Equations

• My weekly paycheck, which was 795 this week,
  included overtime. Normally my paycheck is 625
  w/out OT. How much overtime money did I make
  this week?

Regular Pay Overtime Paycheck
625 x 795
20
Practice Writing Equations

• Team up and do problems 63 70 on page 10.

• 63 70
• x 73 201
• 7x 1596
• 42x 2352
• x 345 987
• 64 19 u or 64 u 19
• 25h 53,400
• 0.27w 56,000,000
• w 1.8 24.5

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Homework

• Login to your MathXL account and do Ch 1 Section
  1 Homework.

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Ch 1 Section 2

• The Commutative, Associative, and Distributive
  Laws

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Commutative, Associative, and Distributive Laws

• These laws tell us what is mathematically legal
  and what isnt.
• These laws allow us to solve equations and
  rearrange formulas.
• Are these statements equivalent?
• 10 5 and 5 10
• 10 ? 5 and 10 ? 5

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Commutative Laws - Defined

• Commute Move
• Addition
• a b b a
• Multiplication
• ab ba

• Is there a commutative law of
• Division?
• Subtraction?

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Examples Commutative Law

• Use the commutative laws to write an expression
  equivalent to each of the following. a) r 7
• b) 12y
• c) 9 st
• Solution
• a) r 7 is equivalent to 7 r
• b) 12y is equivalent to y 12
• c) 9 st is equivalent to st 9

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Associative Laws

• Associate who do you hang-out with?
• Associations are created in math with ( )s.
• Parentheses indicate priority.

(4 8) 5
4 ( 8 5 )
12 5
4 13
17
17
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Associative Laws - Defined

• Addition
• a (b c) a b c
• Multiplication
• a?(b?c) a ? b ? c

( )
( )
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Examples Associative Law

• Use the associative laws to write an expression
  equivalent to each of the following. a) t (4
  y)
• b) (12y)z
• Solution
• a) t (4 y) is equivalent to (t 4) y
• b) (12y)z is equivalent to 12(yz)

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Distributive Law - Introduction

• 4 x 82
• 4(80 2)
• 4(80) 4(2)
• 320 8
• 328

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Distributive Law

• 2 ways to do this 5(4 3)

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Example 1 Distributive Law

• Multiply 4(x 7)
• 4(x 7)

4x 4(7)
4x 28
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Distributive Law - Defined

• For any numbers a,b, and c
• a(b c) ab ac

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Terms

• The plus () sign break up an expression into
  terms.

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Example 2 Distributive Law

• Multiply 7(x y 4z)

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Example 3 Distributive Law

• Multiply (a 3)2

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Terminology

• Given
• 12 x 4 48
• Factors are
• 2?5
• 7y
• 6(x 4)

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Factoring Expressions (Factors)

• Factoring write an equivalent expression as a
  product.
• The distributive property in reverse.
• 5x 5y
• 8y 32w 8

8 ? y 8 ? 4w 8 ? 1
38
Practice

• Team-up and do the following problems.
• Pages 18 and 19
• 2, 4, 5, 17, 24, 30, 40, 57, 63, 69, 73, 82, 88

• associative
• commutative
• distributive

• 5r 10 15t
• x, xyx, and 19
• 7(1 y)
• 5(x 2 3y)
• 5 and x
• 88) (3 a) and (b c)

• 5(1 a)
• x y3
• (x 2) y
• 40) w (v 5) and (5 w) v