Bell Ringer In a factory of 200 people, 120 are men who earn $18 an hour. The women earn $20 an hour. What is the average salary of the employees at the factory? Men: 120 $18 = Women: 80 $20 = Total: $ $1600 = Average: $3760 ÷ 200 = $2160 $1600 $3760 $18.80 an hour

Variables and Expressions

Variable A variable is a letter or symbol that represents a number (unknown quantity). 8 + n = 12

Variable A variable can use any letter of the alphabet. n + 5 x – 7 w – 25

Algebraic Expression a group of numbers, symbols, and variables that express an operation or a series of operations. m + 8 r – 3 3n

Evaluate Expressions Evaluate an algebraic expression – To find the value of an algebraic expression by substituting numbers for variables. m + 8m = 2 r – 3r = = 10 5 – 3 = 2

Simplify Combine like terms and complete all operations Simplify: m m 2 m + 8

The Great Dane Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

Expressions In order to translate a word phrase into an algebraic expression, we must first know some key word phrases for the basic operations.

Words That Lead to Addition Sum More than Increased Plus Altogether Greater Than Add Total

Words That Lead to Subtraction Decreased Less Difference Minus How many more Take away Subtract

Words That Lead to Multiplication Product Times Multiply Of Twice Double Triple

Words That Lead to Division Quotient Divide Divided by Split equally

Multiplication Multiplication expressions should be written in side-by-side form, with the number always in front of the variable. 3a 2t 1.5c 0.4f

Division Division expressions should be written using the fraction bar instead of the traditional division sign.

Addition Phrases 1. 3 more than x x the sum of 10 and a number c 10 + c 3. a number n increased by 4.5 n + 4.5

Subtraction Phrases 1. a number t decreased by 4 t – 4 2. the difference between 10 and a number y 10 – y 3. 6 less than a number z z – 6

Multiplication Phrases 1. the product of 3 and a number t 3t 2. twice the number x 2x 3. 4 times a number e 4e

Division Phrases 1. the quotient of 25 and a number b 25 / b 2. the number y divided by 2 y / divided by g 5 / g

Write Algebraic Expressions for These Word Phrases Ten more than a number n A number w decreased by 5 6 less than a number x A number n increased by 8 The sum of a number n & 9 4 more than a number y n + 10 w - 5 x - 6 n + 8 n + 9 y + 4

Write Algebraic Expressions for These Word Phrases A number s plus 2 A number k decreased by 1 31 less than a number x A number b increased by 7 The sum of a number n & 6 9 more than a number z s + 2 k - 1 x - 31 b + 7 n + 6 z + 9

Write an Algebraic Expression for These Situations Scott’s brother is 2 years younger than Scott The sum of two numbers is 12 The difference between two numbers is 5 s - 2 v + c = 12 m – n = 5