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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

• 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

• 439 (206)

• Multiple Multiplication

• 4(5)(7)(1)

• 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)

• 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

• 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

• Important Note

• Top = Numerator

• Bottom = Denominator

• Zero can never be the Denominator

• That is undefined

• What is 24(32)

• 144

• What is 80

• 1

• What’s 7694/24 ?

• 320r14 or 320.583333333333333333

• Area of a rectangle = length times width

• Area of a square = side times side

• Rate = distance / time

• 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 thru 187 EOO

• 10, 16, 34, 48, 56, 78, 82, 98, 124, 132, 158, 178

Giant Idaho Potato

• 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.

• What you want

• The variable to = a constant

• Like y=5

• What's the opposite of:

• Subtraction

• Multiplication

• Division

• Exponents

• Square Roots

• 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

• Y+5=9

• -5 -5

• Y = 4

• Sub in what you found for Y into the original equation

• Does 4+5 = 9

• You Bet!

• 3=T+1

• It’s the same thing

• 3=T+1

• -1 -1

• 2=T

• 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

• 37 = a + 12

• a=25

• 3z=36

• z=12

• 13+m=13

• m=0

• 70=14n

• n=5

• 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

• Is

• Was

• Is equal to

• Represents

• Is the same as

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

• 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

• 1 thru 40 EOO

• 12, 22, 28, 30, 38, 40