Ch 1.3 – Order of Operations

Objective:

To simplify expressions using the order of operations.

Order of Operations (PEMDAS)

The Order of Operations are rules that explain how to evaluate mathematical expressions.

• Parenthesis

• Exponents

• Multiplication & Division

• Addition & Subtraction

Example

This is WRONG!

1 * 2 + 3 * 4

= 2 + 3 * 4

= 5 * 4

= 20

Multiply – Add – Multiply

NO!

This is CORRECT!

1 * 2 + 3 * 4

= 2 + 12

= 14

Multiply – Multiply - Add

YES!

Order of Operations

Parenthesis

Exponents

6 + 5(6)6 + 30 = 36

2 + 3 252 + 75 = 77

Multiply / Divide8 4 = 32

Add / Subtract10 - 3 + 8

7 + 8 = 15

1) 6 + 5(8 - 2)

2 3 52+ •2)

3) 16 2 4÷ •

4) 10 3 2 4− + •

Try These

Simplify each expression below.

1) 6 + 5(8 - 2)

2 3 52+ •2)

3) 16 2 4÷ •

4) 10 3 2 4− + •

Simplify the following.

1)

2)

3)

4)

( )4 3 6 2 10+ • −

24 2 18 5 1− ÷ +[ ( )]

8 36 4 5− ÷ +

8 5 4

10 6

+ •−

(4 + 18)2 - 10(22)2 - 10

44 - 10 = 34

24 - 2[18 6]

24 - 2[3]

24 - 6 = 18

8 - 9 + 5-1 + 5

4

8 + 204284

= 7

242

2(4 + 8)

Evaluate the expression if a = 2, b = 4, and c = 8

1) ab - c

2) 3a(c - b)

3)

4)

b a+ ÷3 22

2( )b c

a

+

(2)(4) - 88 - 80

3(2)(8 - 4)

3(2)(4)

24

4 + 3(2) 22

4 + 3(4) 2

4 + 6 = 10

22(12)

2= = 12

4 + 12 2

3 + 4 2 =

Fact: Scientific calculators and computers follow the order of operations. Basic calculators do not.

BasicCalculator

ScientificCalculator

Computer

3 + 4 x 2 = 3 + 4 x 2 = *7 x 2 = 14 3 + 8 = 11 3 + 8 = 11

Symbolic Differences in Calculators and Computers

ExpressionScientificCalculator Computer

+

-x

42

++

--*x

/

4 x 2y

4 ^ 2

÷ ÷

Key Sequences and Computer Input

ExpressionCalculator

Key Sequence Computer

3(8 - 2)

4 36 - 2

6 + 8 3 - 1

2

•