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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)

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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


  • Chapter 1 1 3 1 4

    • 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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