### Variables and Expressions

```Variables and Expressions
Chapter 1-1
Prentice Hall Pre Algebra
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
Definitions
◦ a mathematical phrase that uses numerals and
operation symbols.
◦ Is a letter that stands for a number
◦ a mathematical phrase that uses variables,
numerals, and operation symbols.
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
Quick Check

1)
Identify each expression as a numerical expression or a
variable expression. For a variable expression, name the
variable.
8÷x

2)
100 × 6

3)
Numerical expression, no variables
d + 43 – 9

4)
Variable expression, x is the variable
Variable expression, d is the variable
4a

Variable expression, a is the variable
Real-World Problem Solving

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.
1. We know that the dino runs 60 ft in one second.
2. We can label the time in seconds with letter s.
3. We multiply 60ft with by seconds s to find out the
distance the dino runs in s seconds.
• 60 ∙ s or 60s
4. Can you find out how far the dino runs in one minute?
• 360 ft. in one minute
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
Exercises
1.
Write a variable expression for each word
phrase:
a) 10 less than p

p – 10
b) 4 fewer than j

j-4
c) 3 divided by n

3÷n
d) The sum of 18 and c

18 + c or c + 18
Write an expression
1.
The number of days in 4 weeks

2.
The number of days in w weeks

3.
7w
Number of feet in 100 inches

4.
7 ∙ 4 or 4 ∙ 7
100 ÷ 12
Number of feet in i inches

12i
The Order of Operations
Chapter 1-2
Prentice Hall Pre Algebra
Order of Operation
Rule:
1. Parenthesis
2. Exponents
3. Multiplication or Division
 When there are two operation with the
same rank, you need to solve them
from Left to Right.
Example

Using order of
operation
6 + 15 ÷ 3 (divide)
 6+ 5
 11
CORRECT


Not using the order
of operation
6 + 15 ÷ 3 (add)
 21 ÷ 3
(then divide)
 7
WRONG

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

Order of Operation
Rule:
1. Parenthesis
2. Exponents
3. Multiplication or Division
 When there are two operation with the
same rank, you need to solve them
from Left to Right.
Quick Check
4
−1∙2+6÷3
4−2+6÷3
4−2+2
2+2=4
5 + 6 ∙ 4 ÷ 2
5 + 24 ÷ 2 − 3
5 + 12 − 3
17 − 3 = 14
−3
P.E.M.D.A.S.
Insert grouping symbols () to make the
number sentence true:
1. 3 + 5 ∙ 8 = 64

 (3 + 5) ∙ 8 = 64
2.
4 ∙ 8 + 3 = 44
 4 ∙ (8 + 3) = 44
3.
4 ∙ 8 + 6 ÷ 6 − 3 = 34
 4 ∙ 8 + 6 ÷ (6 − 3) = 34
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 − (0.95 + 2 × 0.55)
\$2.95
Solving Problems

What you need to
know to solve this
problem:
◦ Area of a rectangle
is length times
width
◦ A = L xW
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.


Write the
numerical
expression prior
to calculations.
Find more than
one way to solve
the problem.
```