Section 1-1: Using Variables
Objectives: (1) To model relationships
with variables
(2) To model relationships with
equations
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.
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
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
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
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
What Out for Combos!!!
• Ex: The sum of 3 times a number and 7
3x + 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)
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!
Writing Expressions to Represent a
Data Table
Hours Worked
Money Earned
1
18=8
2
2  8 = 16
3
3  8 = 24
7
7  8 = 56
h
8  h = 8h
This is the
expression we are
looking for!
Writing Expressions to Represent a
Data Table
• Find the pattern
• Express the pattern mathematically
– Hence the term expression
• Then you’re done!