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## PowerPoint Slideshow about ' Chapter 1 (1.3,1.4)' - daphne-mcdonald

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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

1.4 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:
- Addition
- 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
- 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

- 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

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