Writing Algebraic Expressions

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

2. Warm Up • 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

3. 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.

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

5. On the back of your notes:

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

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

8. Multiplication Phrases: • Product • Times • Multiply • Of • Twice or double • Triple

9. Division Phrases: • Quotient • Divide • Divided by • Split equally

10. 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

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

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

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

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

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

16. 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

17. 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

18. 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)

19. 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.

20. 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

21. 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

22. 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