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 = 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 ,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 2 3 = 2*2*2 = 8 In a b, a is the base Multiple Exponents (Numbers and Variables) = 1*1*1*1*3*3 c 2 b 3 = 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 2 4( 3 2) 144 What is What’s 7694/24 ? 320r14 or

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 *2 2 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: 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 = X =2

Example Y+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 =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 Is Was Is equal to Represents Is the same as

Examples The product of seven and a number equals twenty-eight. Find the number. Unknown: n The product of seven and a number Equals twenty-eight 7n=28 77 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 thru 40 EOO 12, 22, 28, 30, 38, 40