1. Variable Expressions 2009 SOL A.1
Varina High School
Tammy Wallace

2. Vocabulary
A variable is a symbol, usually a letter, used to represent a unknown quantity.
An algebraic expression may contain numbers, variables, operations, and grouping symbols. An algebraic expression may be evaluated by substituting values for the variables in the expression.

3. How are algebraic expressions used in Algebra?
Algebraic expressions can be translated to verbal expressions or word phrases
Verbal expressions or word phrases, which describe characteristics of given conditions, can also be translated into algebraic expressions for the purpose of evaluation.

4. In expressions, there are many different ways to write multiplication:𝑎𝑏
𝑎∙𝑏
𝑎 𝑏 or 𝑎 𝑏
(𝑎)(𝑏)
𝑎 x 𝑏
We are not going to use the multiplication symbol (#5) any more. Why do you think we will not use this anymore?

5. Division, on the other hand, is written as:
𝑥 3
𝑥÷3

6. Here are some phrases you may have listed. The terms with
Here are some phrases you may have listed. The terms with * are ones that are often used.
Addition
Subtraction
Multiplication
Division
Exponents
 sum
difference
produce
quotient
power of ___
increase 
decrease
times
divided
squared
plus
minus
multiplied
ratio
cubed
add
subtract
more than
less than
total

7. Writing Algebraic Expressions
Steps for Writing Algebraic Expressions:
Read for understanding
Define the variable
Translate the words into numbers/variables/operations
Write as an expression

8. Define a variable and write an algebraic expression for each phrase.
two times a number plus 5  
Read for understanding
Define the variable.
Translate to numbers
Write as an expression
𝟐𝒙+𝟓
two times
a number
plus 5
This can be whatever you want it to be Let x = “a number”
two times
a number
plus 5 2∙ 𝑥 +5

9. 7 less than three times a number
(NOTE: when the words “more than” or “less than” are used, write the expression opposite than how you read it)
Read for understanding
Define the variable
Translate to numbers
Write as an expression
𝟑𝒙−𝟕
7 less than
3 times
a number
Let x = “a number”
7 less than
3 times
a number
𝑠𝑜𝑚𝑒𝑡ℎ𝑖𝑛𝑔 −7 3∙ 𝑥

10. The absolute value of the sum of a number and 5
Read for understanding
Define the variable
Translate to numbers
Write as an expression
𝒙+𝟓
the absolute value of
the sum of
a number and 5
Let x = “a number”
the absolute value of
the sum of
a number and 5 ?
?+?
𝑥 and 5

11. The quotient of a number cubed and 12.
Read for understanding
Define the variable
Translate to numbers
Write as an expression
𝒙 𝟑 𝟏𝟐
quotient of
a number cubed
and 12
Let x = “a number”
quotient of
a number cubed
and 12
? ?
𝑥 3
𝑎𝑛𝑑 12

12. The square root of the product of 6 and a number squared.
Read for understanding
Define the variable
Translate to numbers
Write as an expression
𝟔 𝒙 𝟐
square root of
the product of
6 and a number squared
Let x = “a number”
square root of
the product of
6 and a number squared ?
?∙?
6 and 𝑥 2

13. Write an verbal expression for each algebraic expression
𝟖+𝒂 
Answers may vary

14. Write an verbal expression for each algebraic expression
𝒎 𝟐  
Answers may vary

15. Write an verbal expression for each algebraic expression
𝟑 𝒏 −𝟓
Answers may vary

16. Write an verbal expression for each algebraic expression
𝒙 𝟐 +𝟔
Answers may vary