Go over homework Ch 1 1 Algebraic Expressions

• Go over homework

Ch. 1 -1 Algebraic Expressions and the Order of Operations

Algebra Map In the concept map below, various aspects of algebra are found, as well as how the aspects relate to different parts of "language" such as nouns, verbs, and pronouns.

Different Ways to Show Multiplication: "X" (times sign) 3 x 5 ". " (raised dot) 3 . 5 * (asterisk, used with computers) 3*5 (#)(#) parentheses (3)(5) # next to letter 3 x = (3)(x) letter next to letter xyz = x (y)(z) exponents 23 = 2 x 2 Different Ways to Show Division: Division symbol ( ÷) 2 ÷ 5 Slash symbol ( / ) 2/5 Fraction bar 2 5

Ch. 1 -1 Algebraic Expressions and the Order of Operations -a variable is a symbol that stands for one or more numbers Example: x = 2 y = -4 z = 0 -an algebraic expression is a mathematical phrase that uses numbers variables and operation symbols. Example: x + 2 y – 2 4 x You can translate word phrases into algebraic expressions. 3 more than a number A number increased by 3 x + 3 The quotient of a number and 8 x/8 6 times a number The product of 6 and a number 6 x 15 less than a number 15 subtracted from a number x - 15

• Less. . . Less than. . . Is Less Than Be cautious when you are translating to be exact, especially with the word phrases: "Less, Less than, and Is less than. " Read the follow Common words used in English: Addition Subtraction Multiplication Division Difference Sum Product Minus Quotient of Plus Times Subtracted Divided by Added to Multiply from Into More*, More Twice, Double ( x Less* Per than* 2) Less than * Increased by Triple ( x 3 ) Decreased Total, totaling Of by Five less a number is two. 5 -n=2 Five less than a number is two. n-5=2 Five is less than a number. 5<n

variable A symbol that stands for one or more numbers, like a pronoun x = slope of a line h = height z = 22 t = -55

Algebraic expression mathematical phrase that uses numbers variables and operation symbols, like an incomplete sentence y – 2 x + 2 4 x

Numerical expression mathematical phrase that uses numbers and operation symbols, like an incomplete sentence 5 – 2 2 + 2 4 x 8

Example 1: Write an algebraic expression for each statement below. a. ) At a ballpark, team hats are $15 each. Let n represent the number of hats purchased. 15 n b. ) You lose $5 from your wallet. Let x represent the original amount of money that you started with. x - 5 -to simplify an expression means to replace each variable with its simplest name -to evaluate an expression, replace each variable with a number and then simplify

Simplify means to replace each variable with its simplest name 25 y – 5 y Simplified is 20 y 4 t x 8 Simplified is 32 t 5 x + 2 x Simplified is 7 x

Evaluate n = 4 replace each variable with a number and then simplify n + 5 = 9 6 n = 24 n/4 = 1

Get out whiteboards – Going to practice

1. 5 less than a number n n -5 |n| + 15 2. 15 more than the absolute value of a number 60 n 3. The number of minutes in n hours 4. 5 more than a number, divided by 9 (x+5) / 9 or as a fraction 5. 3 more than the product of 8 and a number 6. 3 less than the absolute value of a number, times 4 8 y +3 4 ( |n| +3 ) 7. The amount of money Waldo has if he has $10 more than Jon 8. The amount of money that Mika has is she has some quarters 9. How much weight Kirk can lift if he lifts 30 lb more than his brother W +30 10. How fast Rya runs if she runs 5 mi/hr slower than Danae J +10. 25 q d-5

1. N / 4 A number divided by four The quotient of a number and four 2. n + 4 4 more than a number The sum of a number and 4 A number increased by 4 3. 3 n The product of 3 and a number Tripled a number or a number tripled 3 times a number 4. N - 8 8 less than a number The difference of a number and 8 A number decreased by 8

Order of Operations: Basically "4" Rules (Do the rules in order): RULE 1 - Do all operations within grouping symbols (parentheses, brackets, vinculum (fraction bar)) RULE 2 - Evaluate the number value for any exponents RULE 3 - Multiply or divide in order from left to right RULE 4 - Add or subtract in order from left to right Example 3: Use the order of operations to simplify each expression below. x = 4 and y = 2 a. ) (x + 4) – 5 + x * 3 b. ) 2 y – x + 8/y Plug in for x and y (4 + 4) – 5 + 4 * 3 Plug in for x and y 2(2) – 4 + 8/2 Simplify using order of operations (8) – 5 + 12 = 15 c. ) xy/2 + 5 – 3 Plug in for x and y 4(2)/2 + 5 - 3 Simplify using order of operations 8/2 + 5 – 3 = 6 Simplify using order of operations 4 – 4 + 4 = 4 d. ) 18 – 3 y + (x – 2) Plug in for x and y 18 – 3(2) + (4 – 2) Simplify using order of operations 18 – 6 + 2 = 14

Example: When there are two or more parenthesis, or grouping symbols, perform the inner most grouping symbol first. 2 + 3[ 5 + (4 - 1)2] 2 + 3[ 5 + (3)2] inner most parentheses are done first 2 + 3[ 5 + 9] then work your way out 2 + 3[ 14] 2 + 42 44

Classwork – Textbook p 7 1 -5 C 3 Section 1. 1 Homework– Textbook page 7 -8; 6 -24 evens show work for each problem or no points Problems 6, 8, 18 do not need to show work put a circle around the problem number