Chapter 1: Whole Numbers

1
Chapter 1 Whole Numbers

• Order of Operations

2
Order of Operations

• Whenever you solve a math problem, you must use
  the following order of operations.
• parentheses or groupings (), ,
• exponents or roots
• divide or multiply
• subtract or add

3
Order of Operations

• Use the convenient phrase
• Please
• Excuse
• My Dear
• Aunt Sally
• to remember the order of operations

4
Order of Operations

• Please parentheses or groupings
• Excuse exponents
• My Dear multiply or divide
• Aunt Sally add or subtract

5
Order of Operations

• P
• Please parentheses or groupings (), ,
• ( ) means parentheses
• means bracket
• means brace
• Do what is in ( ) first, then do what is in ,
  and finally do what is in .

6
Order of Operations

• E
• Excuse exponents or roots
• Exponents (Exponential Notation)
• 73 7 7 7 343
• 25 5

7
Order of Operations

• M D
• Everything is done from left to right from this
  point on.
• My or Dear divide or multiply or multiply or
  divide from left to right.

8
Order of Operations

• A S
• Everything is done from left to right from this
  point on.
• Aunt or Sally subtract or add or add or subtract
  left to right.

9
Order of Operations

• Please parentheses or groupings
• Excuse exponents
• My Dear multiply or divide
• Aunt Sally add or subtract

10
Order of Operations

• 21 14 ? 7 - 2

21 14 ? 7 - 2
1. Divide 14 by 7
21 2 - 2
21 2 - 2
2. Do Addition Subtraction in order from left
to right
23 - 2
23 - 2
21
11
Order of Operations
(21 14) ? 7 - 2
(21 14)
1. Do Parentheses
(35) ? 7 - 2
(35) ? 7 - 2
(35) ? 7 - 2
2. Remove the Parentheses
5 - 2
5 - 2
3. Divide 35 by 7
3
4. Subtract 2 from 5
12
Order of Operations
21 14 ? 7 - 2
(21 14) ? 7 - 2
21
3
Note how the order of operations can lead to
different answers with the same set of numbers.
13
Order of Operations
8 24 42
8 24 42
1. Do Exponents
8 16 16
8 16 16
2. Do Multiplication Division in order from
left to right.
128 16
128 16
8
14
Order of Operations
1. Do Exponents
4(5) - 16
4(5) - 16
2. Do Multiplication
20 - 16
20 - 16
3. Do Subtraction
4
15
Order of Operations
5 420 - 2(7 - 2)
1. Do Parentheses
5 420 - 2(7 - 2)
2. Do Brackets a. Multiply b. Subtract
5 420 - 2(5)
5 420 - 2(5)
5 420 - 10
5 420 - 10
5 410
5 410
3. Do Multiplication
4. Do Addition
5 40
5 40
45
16
Order of Operations
4 218 - 3(5 - 2)
4 218 - 3(5 - 2)
1. Do Parentheses
2. Do Brackets a. Multiply b. Subtract
4 218 - 3(3)
4 218 - 3(3)
4 218 - 9
4 218 - 9
4 29
4 29
3. Do Multiplication
4. Do Addition
4 18
4 18
45
17
Order of Operations
A Prize Winning Problem

• 12 34(36 - 15) ? 3 2 2

12 3421 ? 3 2 2
12 347 2 2
12 349 2
12 336 2
12 338
12 114
126