Order of Operations in Math: Rules & Examples

Lesson Overview

• What Is the Order of Operations?
• How to Remember the Order of Operations
• Order of Operations Rules:
• Order of Operations: PEMDAS vs BODMAS
• How to Remember the Order of Operations
• Order of Operations Assessment

Math problems sometimes have lots of steps. Adding, subtracting, multiplying-it can get confusing which to do first! Luckily, there's a set of rules called the Order of Operations that helps solve problems the right way every time.

Imagine you're planning a pizza party for your friends. You need to figure out how many slices everyone will get. This involves some math, and that's where the order of operations comes in handy. 

What Is the Order of Operations?

To solve math problems correctly, we need to follow a special order of operations. This is where PEMDAS (or BODMAS) comes to the rescue-it helps you solve the problem step by step! 

BODMAS is also another acronym used to remember the order of operations, but it is mainly used in the United Kingdom and India.

How to Remember the Order of Operations

To remember the order, remember this phrase: "Please Excuse My Dear Aunt Sally". The first letter of each word helps you remember the PEMDAS" easily.

Children can create favorite phrases to help remember the order of operations in math. For example: "Pick Every Meal Delicious And Sweet!"

Let's try an example: 5 + 2 x (7 - 3)²

1. Parentheses First!

(7 - 3) = 4

2. Exponents Next!

4² = 4 x 4 = 16

3. Multiplication!

2 x 16 = 32

4. Finally, Addition!

5 + 32 = 37

So, the answer is 37!

Addition Tips:

• Write down the order of operations (PEMDAS) at the top of your paper to help you remember.
• Go step-by-step and show your work. This will help you avoid mistakes.

Order of Operations Rules:

Take this Quiz :

Maths Quiz For 5th Grade - Order of Operations

1. P for Parentheses ( ):  Anything inside parentheses or brackets [ ] gets solved first.
   
   • Example: 3 + (4 - 2)
     • Solve 4 - 2 first, which equals 2.
     • Then, 3 + 2 = 5
       
2. E for Exponents:  These are the tiny numbers above a bigger number. They tell you how many times to multiply the big number by itself.
   • Example: 2 x 3²
     • Solve 3² first, which equals 9 (3 x 3).
     • Then, 2 x 9 = 18
       
3. MD for Multiplication and Division: These two are partners in crime. Solve them from left to right.
   
   • Example: 10 ÷ 2 x 5
     • Solve 10 ÷ 2 first, which equals 5.
     • Then, 5 x 5 = 25
       
4. As for Addition and Subtraction: Another dynamic duo! Solve them from left to right.
   
   • Example: 8 - 3 + 5
     • Solve 8 - 3 first, which equals 5.

Then, 5 + 5 = 10

Order of Operations: PEMDAS vs BODMAS

Example:

8 + (2 × 3)² ÷ 2

Solution Using Both

• PEMDAS:
  
  1. Parentheses: 2 × 3 = 6.
  2. Exponents: 6² = 36.
  3. Division: 36 ÷ 2 = 18.
  4. Addition: 8 + 18 = 26.
     
• BODMAS:
  
  1. Brackets: 2 × 3 = 6.
  2. Orders: 6² = 36. 
  3. Division: 36 ÷ 2 = 18.
  4. Addition: 8 + 18 = 26.
     

The outcomes of both scenarios are same.

How to Remember the Order of Operations

Take this Quiz :

Order of Operations Quiz Questions and Answers

Solved Example On Order of Operations

7 + (6 x 3²) - 4 ÷ 2

Apply (PEMDAS): 

1. P for parentheses: We have parentheses!
   
   • 6 x 3² (We need to do the exponent first!)
   • 3² = 3 x 3 = 9
   • 6 x 9 = 54
     
2. E for Exponents: We already took care of the exponent in step 1!
   
3. MD for Multiplication and Division (from left to right):
   
   • We did the multiplication in the parentheses already. Now we have division: 4 ÷ 2 = 2
     
4. AS for Addition and Subtraction (from left to right):
   
   • Now we have: 7 + 54 - 2
   • 7 + 54 = 61
   • 61 - 2 = 59

Here's how it looks all together:

7 + (6 x 3²) - 4 ÷ 2 = 7 + (6 x 9) - 4 ÷ 2 = 7 + 54 - 4 ÷ 2 = 7 + 54 - 2 = 61 - 2 = 59

Order of Operations Assessment

1. Solve the equation: 15 - 6 ÷ 3 + 2 x 4 = ?
2. Solve the equation: (8 + 5) x 2 - 10 ÷ 5 = ?
3. Find the Missing Number: 3² + 12 ÷ (6 - 3) x 2 = ?
4. Find the Missing Number: 20 - 4 x 3 + 2³ ÷ 4 = ?

Answers to Assessment: 

1. 15 - 6 ÷ 3 + 2 x 4 = 21
   
   • 15 - 2 + 2 x 4
   • 15 - 2 + 8
   • 13 + 8 = 21
     
2. (8 + 5) x 2 - 10 ÷ 5 = 24
   
   • 13 x 2 - 10 ÷ 5
   • 13 x 2 - 2
   • 26 - 2 = 24
     
3. 3² + 12 ÷ (6 - 3) x 2 = 17
   
   • 3² + 12 ÷ 3 x 2
   • 9 + 12 ÷ 3 x 2
   • 9 + 4 x 2
   • 9 + 8 = 17
     
4. 20 - 4 x 3 + 2³ ÷ 4 = 14
   
   • 20 - 4 x 3 + 8 ÷ 4
   • 20 - 12 + 8 ÷ 4
   • 20 - 12 + 2
   • 8 + 2 = 14