Transcript Chapter 1 (1.3,1.4,1.5)

Chapter 1 (1.3,1.4)
The End of the Beginning
1.3 Multiply and Divide
 Multiplication = Repeated addition of the
same number

2 times 3 = 2 + 2 + 2
 The numbers being multiplied = factors
 The answer to a multiplication problem =
product
 Ways to show multiplication
Dot
Parenthesis (on one of all of the factors)
4(7) or (4)(7)
Nothing ( like 3 times B is 3B)
Big Problems
 439 (206)
 Multiple Multiplication
 4(5)(7)(1)
Properties of Multiplication
 1. If you multiply by zero, you get zero
 2. If you multiply a factor by one, you get that factor
 4x=4
x=1
 3. If you have a problem where everything is being
multiplied (i.e. no addition, subtraction, etc.) the
order in which you multiply does not matter.
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(2*3)4 = 2(3*4)
Try a few
 Find the product of 8,704 and 93
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809,472
 Evaluate 8ab when a = 4 and b = 2
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8*4*2 = 8 * 8 = 64
 What’s 70 * 9,000 (Hint, there is a shortcut)
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Take 7 * 9 and add 4 zeros = 630,000
 Is 11 a solution for 11x = 121
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Yes because 11*11 = 21
Exponents
 That little number at the top right
 23 = 2*2*2 = 8
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In ab, a is the base
 Multiple Exponents (Numbers and Variables)
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1432 = 1*1*1*1*3*3
c2b3 = c*c*b*b*b
Division
 Important Note
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Top = Numerator
Bottom = Denominator
Zero can never be the Denominator
 That is undefined
Try a few more
 What is 24(32)
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144
 What is 80
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1
 What’s 7694/24 ?
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320r14 or 320.583333333333333333
Applications and formulas
 Area of a rectangle = length times width
 Area of a square = side times side
 Rate = distance / time
Prime Factorization
 Use your method or the Tree method
 Prime number  Divisible by 1 and itself.
 12 = 3 * 4 = 3 *2*2 = 3 *22
 Question: What is the exponent on the 3?
 Try 56, 28

Note: Factors are all the different possibilities
1.3 Homework
 1 thru 187 EOO
 10, 16, 34, 48, 56, 78, 82, 98, 124, 132, 158,
178
Giant
Idaho
Potato
1.4 Equations
 Equations have an equals sign!

x+ 3 = 7
 Remember solving algebraic equations is all
about opposites.
 i.e. do the opposite of the whatever the
mathematical operation.
Solving Stuff
 What you want

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The variable to = a constant
Like y=5
 What's the opposite of:
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Addition
Subtraction
Multiplication
Division
Exponents
Square Roots
First form
 X+a=b
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X+3=5
Try to get simplify first (PEMDAS)
Try to isolate the variable
Do the opposite
X+3 =5
-3 -3
X =2
Example
 Y+5=9
 -5 -5
 Y =4
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Check your answer
Sub in what you found for Y into the original equation
Does 4+5 = 9
You Bet!
Things are what they appear
 3=T+1
 It’s the same thing

3=T+1
 -1
-1

2=T
 Check your answer
The second type
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Form ax=b
2x=6
What’s the operation between the 2 and the x?
What's the opposite?
Do it!
2x=6
2 2
x=3
Try a few
 37 = a + 12
 a=25
 3z=36
 z=12
 13+m=13
 m=0
 70=14n
 n=5
Turning Words into Numbers and
Letters
 Take these piece by piece and they will be
much much easier!
 3 Part process
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Assign a variable to one of the unknowns
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Use that variable to write an expression for
any other unknowns
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Write the variable expression
Equals
 Equals
 Is
 Was
 Is equal to
 Represents
 Is the same as
Examples
 The product of seven and a number equals
twenty-eight. Find the number.
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Unknown: n
The product of
seven and a
number
Equals
7n
=
7
n
twenty-eight
28
7
=
4
Try Some
 Twelve added to a number is sixty. Find that number.
 48
 Using the formula A = P + I, where A is the investment
value, P is the original investment, and I is the
interest, to find the interest earned on an original
investment of $18,000 that now has a value $21,060.
 $3,060
 The sum of eleven and a number equals fifty-two.
Find that number
 41
Homework 1.4
 1 thru 40 EOO
 12, 22, 28, 30, 38, 40