Writing Algebraic Expressions Objective: Be able to write an algebraic expression for a word phrase or write a word phrase for an expression.

Warm Up ) 7x + 4 for x = 6 2.) 8y – 22 for y = 9 46 Evaluate each algebraic expression for the given value of the variables. ) 7x + 4 for x = 6 2.) 8y – 22 for y = 9 3.) 12x( )for x = 7 and y = 4 4.) y + 3z for y = 5 and z = 6 46 50 8 y 86 23

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.

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

On the back of your notes: Addition Subtraction Multiplication Division

Addition Phrases: More than Increase by Greater than Add Total Plus Sum

Subtraction Phrases: Decreased by Difference between Take Away Less Less than* Subtract from*

Multiplication Phrases: Product Times Multiply Of Twice or double Triple

Division Phrases: Quotient Divide Divided by Split equally

Notes 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

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

Examples Addition phrases: 3 more than x the sum of 10 and a number c a number n increased by 4.5

Examples Subtraction phrases: a number t decreased by 4 the difference between 10 and a number y 6 less than a number z

Examples Multiplication phrases: the product of 3 and a number t twice the number x 4.2 times a number e

Examples Division phrases: the number y divided by 2 2.5 divided by g the quotient of 25 and a number b the number y divided by 2 2.5 divided by g

Examples converting f feet into inches a car travels at 75 mph for h hours the area of a rectangle with a length of 10 and a width of w

Examples converting i inches into feet the cost for tickets if you purchase 5 adult tickets at x dollars each the cost for tickets if you purchase 3 children’s tickets at y dollars each

Examples the total cost for 5 adult tickets and 3 children’s tickets using the dollar amounts from the previous two problems (problems e and f)

Write a variable expression to represent the following if x represents your age. 1) Your age 5 years ago. 2) Twice your age. 3) Your age in 8 years.

Translate the following phrases. 1) Five plus x minus 3 5 + x - 3 2) Three times y less 4 3) Eight multiplied by y minus 7 8y - 7 4) The product of 10 and m decreased by 7 10m - 7 5) Four more than the quotient of x and 3 6) Six times m plus 8 6m + 8

Define a variable to represent the unknown and write the phrase as a variable expression. 1) 10 mph faster than the Honda Let x = the speed of the Honda x + 10 2) 7 inches shorter than Jill’s brother Let b = the height of Jill’s brother b - 7 3) 5 acres larger than twice the size of my lot Let k = the size of my lot 2k + 5 4) $7.50 times the number of people plus a $20 group registration Let y = the number of people $7.5y + $20

Match each phrase with its variable expression. d 1) Twice the sum of x and 3 e 2) Two less than the product of 3 and x b 3) Three times the difference of x and 2 a 4) Twice a number x less 3 c 5) Two more than 3 times a number x