1. Section 1-1: Using Variables
Objectives: (1) To model relationships with variables
(2) To model relationships with equations

2. Definitions
A variable is a symbol, usually a letter, that represents one or more numbers.
An algebraic expression is a mathematical phrase that can include numbers, variables and operational symbols.
An equation is a mathematical statement that says two or more expressions are equal.

3. Applying Words to Symbols
Addition
Sum
Ex: The sum of a 12 and a number
12 + x
More than
Ex: 3 more than a number
x + 3
Plus
Ex: a number plus 6
n + 6

4. Applying Words to Symbols (Cont’)
Subtraction
Difference
Ex: The difference of a number and 8
x – 8
Less than
Ex: A number less than 7
7 – x
Decreased by
Ex: 10 decreased by a number.
10 – y
Subtracted From
5 subtracted from a number
x – 5

5. Applying Words to Symbols (Cont’)
Multiplication
Times
Ex: A number times 5
x  5
Multiplied By
Ex: 2 multiplied by a number
2  x
Product
Ex: the product of a number and 4
x  4 Of
Ex: one-fifth of a number
1/5 x

6. Applying Words to Symbols (Cont’)
Division
Quotient
Ex: The quotient of 3 and a number
3/x or 3 ÷ x
Divided by
Ex: A number divided by 9
x/9 or x ÷ 9

7. What Out for Combos!!! Ex: The sum of 3 times a number and 7
Ex: Twice a number divided by 3
2x/3
Ex: 1/8 of a number
1/8 x
Ex: 4 times the sum of a number and 2
4  (x + 2)

8. Writing Expressions to Represent a Data Table
Suppose you had a job that paid $8 an hour. How much money would you make in an hour?
If you said $8, you’d be correct.
How much would you make in 3 hours? 7 hours?
If you said, “$24 and $56” you be correct again.
Pat yourself on the back!

9. Writing Expressions to Represent a Data Table
Hours Worked
Money Earned 1
1  8 = 8 2
2  8 = 16 3
3  8 = 24
7  8 = 56 7
8  h = 8h h
This is the expression we are looking for!

10. Writing Expressions to Represent a Data Table
Find the pattern
Express the pattern mathematically
Hence the term expression
Then you’re done!