IS means = sign Writing Equations: “2 more than twice a number is 5” 2 + 2x = 5 2 + 2x = 5 Sometimes you have to decide what the variable is… It can be any letter. We usually see x and y used as variables. “a number divided by 3 is 8” x 3 = 8 or

Now you try… “the sum of a number and ten is the same as 15” x + 10 = 15

Now you try… “The total pay is the number of hours times 6.50” {Sometimes, two variables are needed}

Writing an Equation… Define variables and identify key parts of the problem… Track One Media sells all CDs for $12 each. Write an equation for the total cost of a given number of CDs.

Let's look at another... Number of CDs Cost 1 $8.50 2 $17.00 3 $25.50 4 $34.00 This table shows the relationship between number of CDs and cost. How much is 1 CD? T = $8.50n

C = total cost for CDs n = number of CDs bought C = 8.50 n 1 $8.50 2 $17.00 3 $25.50 4 $34.00 Cost = $8.50 times (number of CDs) C = total cost for CDs n = number of CDs bought C = 8.50 n

We use a table of values to represent a relationship. Number of hours Total pay in dollars 5 40 10 80 15 120 20 160 From the table, we can come up with an equation. Total pay = (number of hours) times (hourly pay) What is the hourly pay? $8 per hour Total pay = 8 (number of hours) T = 8h

Write an equation for the data below… # of Hours Total Pay 8 $40 12 $60 16 $80

Exponents and Order of Operations Math 1 Sept 9

Perform the indicated operations Check your skills Find each Product 4 x4 7 x 7 5 x 5 9 x 9 Perform the indicated operations 3 + 12 – 8 4 – 2 + 9 5 x 5 + 7 30 ÷ 6 x 2

To simplify an expression, we write it in the simplest form. Example: Instead of 2 + 3 + 5, we write 10. Instead of 2 · 8 + 2 · 3, we write 22. We use order of operations to help us get the right answer. PEMDAS Parentheses first, then exponents, then multiplication and division, then addition and subtraction. In the above example, we multiply first and then add.

A power has two parts, a base and an exponent, such as An exponent tells you how many times to multiply a number (the base) by itself. Means 2 times 2 times 2 times 2 Or 2 · 2 · 2 · 2 This is also read as “2 to the 4th power” A power has two parts, a base and an exponent, such as is 16 in simplest form.

Order of Operations Perform any operations inside grouping symbols first. i.e brackets, parenthesis, curly lines. Simplify powers Multiply and Divide left to right Add and Subtract left to right

PLEASE EXCUSE MY DEAR AUNT SALLY Always follow order of operations starting with the inside parentheses. PLEASE EXCUSE MY DEAR AUNT SALLY P Parentheses E Exponents M Multiplication D Division A Addition S Subtraction Left to right when multiplication and division are the only operations left in the problem } } Left to right when addition and subtraction are the only operations left in the problem

Simplifying a Numerical Expression Numerical Expression = a expression with numbers only Simplify: 25 – 8 × 2 + 32 25 – 8 × 2 + (3× 3) 25 – 8 × 2 + 9 25 – 16 + 9 18

Simplify an expression... 6 – 10 ÷ 5 3 * 6 – 42 ÷ 2 4 * 7 + 4 ÷ 22 53 + 90 ÷ 10 4 10 29 134 Remember order of operation

We evaluate expressions by plugging numbers in for the variables. Example: Evaluate the expression for c = 5 and d = 2. 2c + 3d 2(5) + 3(2) 10 + 6 16

Simplifying an Expression With Parentheses When you simplify expressions with parentheses, work within the parentheses FIRST. Lets Try! Simplify: 15(13 - 7) ÷ (8 – 5) 15(13-7) ÷ (8 -5) = 15(6) ÷ 3 = 90 ÷ 3 = 30

Evaluate for x = 11 and y = 8 (11)(8)2 (11)(8×8) (11)(64) = 704

Now you Try: (5 + 3) ÷ 2 + (52 – 3) 8 ÷ (9 – 7) + (13 ÷ 2)

Evaluating Expressions with Exponents The base for an exponent is the number, variable, or expression directly to the left of the exponent. For example: B2  the base would be “B” for exponent “2” 63  the base for “3” would be “6”

Now you try… Evaluate the expression if m = 3, p = 7, and q = 4

Now you try… Evaluate the expression if m = 3, p = 7, and q = 4