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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

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chapter 1 1 3 1 4

Chapter 1 (1.3,1.4)

The End of the Beginning

1 3 multiply and divide
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
slide3
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
Big Problems
  • 439 (206)
  • Multiple Multiplication
  • 4(5)(7)(1)
properties of multiplication
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.
      • (2*3)4 = 2(3*4)
try a few
Try a few
  • Find the product of 8,704 and 93
    • 809,472
  • Evaluate 8ab when a = 4 and b = 2
    • 8*4*2 = 8 * 8 = 64
  • What’s 70 * 9,000 (Hint, there is a shortcut)
    • Take 7 * 9 and add 4 zeros = 630,000
  • Is 11 a solution for 11x = 121
    • Yes because 11*11 = 21
exponents
Exponents
  • That little number at the top right
  • 23 = 2*2*2 = 8
    • In ab, a is the base
  • Multiple Exponents (Numbers and Variables)
    • 1432 = 1*1*1*1*3*3
    • c2b3 = c*c*b*b*b
division
Division
  • Important Note
    • Top = Numerator
    • Bottom = Denominator
    • Zero can never be the Denominator
        • That is undefined
try a few more
Try a few more
  • What is 24(32)
    • 144
  • What is 80
    • 1
  • What’s 7694/24 ?
    • 320r14 or 320.583333333333333333
applications and formulas
Applications and formulas
  • Area of a rectangle = length times width
  • Area of a square = side times side
  • Rate = distance / time
prime factorization
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
1.3 Homework
  • 1 thru 187 EOO
  • 10, 16, 34, 48, 56, 78, 82, 98, 124, 132, 158, 178

Giant Idaho Potato

1 4 equations
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
Solving Stuff
  • What you want
      • The variable to = a constant
      • Like y=5
  • What\'s the opposite of:
      • Addition
      • Subtraction
      • Multiplication
      • Division
      • Exponents
      • Square Roots
first form
First form
  • X+a=b
      • 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
Example
  • Y+5=9
  • -5 -5
  • Y = 4
  • 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
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
The second type
  • 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 few1
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
Turning Words into Numbers and Letters
  • Take these piece by piece and they will be much much easier!
  • 3 Part process
    • Assign a variable to one of the unknowns
    • Use that variable to write an expression for any other unknowns
    • Write the variable expression
equals
Equals
  • Equals
  • Is
  • Was
  • Is equal to
  • Represents
  • Is the same as
examples

The product of seven and a number

Equals

twenty-eight

7n

=

28

7

7

Examples
  • The product of seven and a number equals twenty-eight. Find the number.
    • Unknown: n

n = 4

try some
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
Homework 1.4
  • 1 thru 40 EOO
  • 12, 22, 28, 30, 38, 40
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