Chapter 1 (1.3,1.4)

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# Chapter 1 (1.3,1.4) - PowerPoint PPT Presentation

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)

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.
• (2*3)4 = 2(3*4)
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
• 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
• Important Note
• Top = Numerator
• Bottom = Denominator
• Zero can never be the Denominator
• That is undefined
Try a few more
• What is 24(32)
• 144
• What is 80
• 1
• What’s 7694/24 ?
• 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
• The variable to = a constant
• Like y=5
• What\'s the opposite of:
• Subtraction
• Multiplication
• Division
• Exponents
• Square Roots
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
• Y+5=9
• -5 -5
• Y = 4
• 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
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 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
• 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
• Is
• Was
• Is equal to
• Represents
• Is the same as

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
• 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