1. Variables and Expressions
Chapter 1-1
Prentice Hall Pre Algebra
8th Grade Math

2. Check Skills You’ll Need
How many days in a week?
7 days in a week
How many inches in a foot?
12 inches in a foot
How many cents is a nickel?
a nickel is 5 cents
How many quarts is a gallon?
4 quarts is a gallon
How many feet is a yard?
3 feet is a yard

3. Definitions NUMERICAL EXPRESSION VARIABLE VARIABLE EXPRESSION
a mathematical phrase that uses numerals and operation symbols.
VARIABLE
Is a letter that stands for a number
VARIABLE EXPRESSION
a mathematical phrase that uses variables, numerals, and operation symbols.

4. Examples
Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable.
7 – 5
Numerical expression
a + 4
Variable expression
a is the variable

5. Quick Check
Identify each expression as a numerical expression or a variable expression. For a variable expression, name the variable.
8 ÷ x
Variable expression, x is the variable
100 × 6
Numerical expression, no variables
d + 43 – 9
Variable expression, d is the variable 4a
Variable expression, a is the variable

6. Real-World Problem Solving
Science
The fastest dinosaur may have been Ornithomimus, which could run about 60 ft. in a second. Write a variable expression for the distance Ornithomimus could run in a given time.
We know that the dino runs 60 ft in one second.
We can label the time in seconds with letter s.
We multiply 60ft with by seconds s to find out the distance the dino runs in s seconds.
60 ∙ s or 60s
Can you find out how far the dino runs in one minute?
360 ft. in one minute

7. Quick Check
Bagels cost $.50 each. Write a variable expression for the cost of b bagels.
0.50b
Write a variable expression for the number of hours in m minutes.
60h

8. Exercises Write a variable expression for each word phrase:
10 less than p
p – 10
4 fewer than j
j - 4
3 divided by n
3 ÷ n
The sum of 18 and c
18 + c or c + 18

9. Write an expression The number of days in 4 weeks
7 ∙ 4 or 4 ∙ 7
The number of days in w weeks 7w
Number of feet in 100 inches
100 ÷ 12
Number of feet in i inches
12i

10. The Order of Operations
Chapter 1-2
Prentice Hall Pre Algebra
8th Grade Math

11. Order of Operation Rule: Parenthesis Exponents
Multiplication or Division
Addition or Subtraction
When there are two operation with the same rank, you need to solve them from Left to Right.

12. Example Using order of operation 6 + 15 ÷ 3 (divide) 6 + 5 (then add)11
CORRECT
Not using the order of operation
÷ 3 (add)
21 ÷ 3 (then divide) 7
WRONG

13. Example
18 ÷ 3 ∙ 2
Same rank operation therefore solve from left to write (division first)
6 ∙ 2 12
CORRECT
18 ÷ 3 ∙ 2
Not using order of operation and doing the multiplication first.
18 ÷ 6 3
WRONG

14. Order of Operation Rule: Parenthesis Exponents
Multiplication or Division
Addition or Subtraction
When there are two operation with the same rank, you need to solve them from Left to Right.

15. Quick Check 4 − 1 ∙ 2 + 6 ÷ 3 5 + 6 ∙ 4 ÷ 2 − 3 4 − 2 + 6 ÷ 3
4 − 2 + 2
2 + 2 = 4
5 + 6 ∙ 4 ÷ 2 − 3
÷ 2 − 3
− 3
17 − 3 = 14

16. P.E.M.D.A.S.
Insert grouping symbols () to make the number sentence true:
3 + 5 ∙ 8 = 64
(3 + 5) ∙ 8 = 64
4 ∙ = 44
4 ∙ (8 + 3) = 44
4 ∙ ÷ 6 − 3 = 34
4 ∙ ÷ (6 − 3) = 34

17. Problem
A customer buys orange juice for $.95 and two apples for $.55 each. She gives the cashier a five dollar bill. How much change should the cashier give the customer? (write the numerical expression and than solve the problem)
5 − ( × 0.55)
$2.95

18. Solving Problems What you need to know to solve this problem:
Area of a rectangle is length times width
A = L x W
Write the numerical expression prior to calculations.
Find more than one way to solve the problem.
Urban Planning
Some urban planners specialize in planning entire new towns. These towns are designed for livability, with plenty of open space. The sketch shows the dimensions for a new town called Panorama. Find Panorama’s area.