Transcript 1.3: Order of Operations

1.3 Order of Operations
What you should learn
GOAL
1
Use the order of operations to evaluate
algebraic expressions.
GOAL
2
Use a calculator to evaluate real-life
expressions such as calculating sales tax.
Why you should learn it
To solve real-life problems, such as calculating the
cost of admission for a family to a state fair.
1.3 Order of Operations
GOAL
1
USING THE ORDER OF OPERATIONS
WHAT IS THE ORDER OF OPERATIONS?
It’s the method we use to evaluate an expression
involving more than one operation:
1. Grouping symbols (innermost first, work to the outermost)
2. Powers
3. Multiplication and division left to right
4. Addition and subtraction left to right
Extra Example 1
Evaluate the expression when x = 3.
1. 4 x 2  8
2. 27  x 2  3
4(3)2  8
27  32  3
4(9)  8
27  9  3
33
36  8
28
6
What happens when operations that have the same priority
appear in the same expression, such as 5 – 4 +1?
5–4+1
1+1
5–4+1
Which is
correct?
2
5–5
0
Perform the operations from
left to right!
EXAMPLE 2
Summary
ORDER OF OPERATIONS
1. Perform operations within grouping symbols, beginning
with the innermost first.
2. Simplify powers.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.
EXAMPLE 3
Extra Example 3
Simplify the expression.
Hint: The fraction bar
serves as a grouping
symbol. Simplify the
numerator and
denominator
separately before the
final step.
Click to see each step.
24  3
5  32  2
24  3
592
72
592
72
14  2
Simplify the power.
Simplify the numerator.
Work from left to right.
72
12
Subtract.
6
Simplify.
Checkpoint
1. Evaluate the expression when x = 5.
b. 100 ÷ x2 + 6
10
a. 2x2 + 8
58
2. Simplify the expression.
a. 25 + 10 – 8
27
b. 24 ÷ 2 • 3
36
3. Simplify the expression.
16  2  8
10  22  4
4
c. 36 – 6 ÷ 3 + 3
37
1.3 Order of Operations
GOAL
2
EVALUATING EXPRESSIONS WITH A
CALCULATOR
The point: YOU must know how your calculator works. Be
sure you work through the examples and understand
YOUR calculator.
EXAMPLE 4
EXAMPLE 5
Checkpoint
Simplify each expression using your calculator. Identify the
order in which the operations are performed.
1. 10.5  4.2  1.4  3.5
11; division, subtraction, addition
2. (10.5  4.2)  1.4  3.5
8; subtraction, division, addition
3. (10.5  4.2)  (1.4  3.5)
≈1.29; subtraction, addition, division
QUESTIONS?