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 ) 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

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:
Addition
Subtraction
Multiplication
Division

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

7. Subtraction Phrases: Decreased by Difference between Take Away Less
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 t c f

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 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

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