Mixed Operations and BODMAS

P6 Mathematics - Term I, Topic 3

Lesson 5 of 5

Learning Objectives:

• Apply BODMAS/DMAS rules correctly
• Solve problems with mixed operations
• Use brackets to change calculation order

The Problem!

What is 5 + 3 × 2?

Think about it...

• Is it 16? (If we do 5 + 3 = 8, then 8 × 2 = 16)
• Is it 11? (If we do 3 × 2 = 6, then 5 + 6 = 11)

Which answer is correct?

We Need a Rule!

Without rules, mathematics would be confusing!

Another example: 20 - 4 ÷ 2

• Could be 8 (20 - 4 = 16, then 16 ÷ 2 = 8)
• Could be 18 (4 ÷ 2 = 2, then 20 - 2 = 18)

We need BODMAS to tell us the correct order!

Introducing BODMAS!

The Order of Operations

B - Brackets (do these first!)
O - Orders (powers/squares - P7 level)
D - Division
M - Multiplication
A - Addition
S - Subtraction

Remember: D and M are equal (left to right)
Remember: A and S are equal (left to right)

DMAS - Simpler Version

For P6, we focus on:

D - Division (÷)
M - Multiplication (×)
A - Addition (+)
S - Subtraction (-)

Rule: Division and Multiplication BEFORE Addition and Subtraction!

Let's Solve: 5 + 3 × 2

Using BODMAS

5 + 3 × 2

Step 1: Multiply first (3 × 2 = 6)
Step 2: Then add (5 + 6 = 11)

Answer: 11

Multiplication before Addition!

Let's Solve: 20 - 12 ÷ 4

Using BODMAS

20 - 12 ÷ 4

Step 1: Divide first (12 ÷ 4 = 3)
Step 2: Then subtract (20 - 3 = 17)

Answer: 17

Division before Subtraction!

More Complex Example

Calculate: 6 + 8 × 5 - 10 ÷ 2

Step 1: Multiply (8 × 5 = 40)
Step 2: Divide (10 ÷ 2 = 5)
Step 3: Add (6 + 40 = 46)
Step 4: Subtract (46 - 5 = 41)

Answer: 41

Do all × and ÷ first (left to right), then + and - (left to right)

The Power of Brackets! ()

Brackets Change Everything!

Brackets say: "Do me FIRST, no matter what!"

Example:

• Without brackets: 5 + 3 × 2 = 11
• With brackets: (5 + 3) × 2 = 16

Brackets can completely change the answer!

Example with Brackets

Calculate: (5 + 3) × 2

Step 1: Brackets first! (5 + 3 = 8)
Step 2: Then multiply (8 × 2 = 16)

Answer: 16

Compare:

• 5 + 3 × 2 = 11
• (5 + 3) × 2 = 16

Same numbers, different answers!

Another Bracket Example

Calculate: (20 - 8) ÷ 4 + 6

Step 1: Brackets (20 - 8 = 12)
Step 2: Divide (12 ÷ 4 = 3)
Step 3: Add (3 + 6 = 9)

Answer: 9

Complex Bracket Example

Calculate: 100 - (25 + 15) × 2

Step 1: Brackets first! (25 + 15 = 40)
Step 2: Multiply (40 × 2 = 80)
Step 3: Subtract (100 - 80 = 20)

Answer: 20

Always do brackets FIRST!

The BODMAS Steps

Remember These in Order:

1. Brackets - Do anything in ( ) first
2. Division & Multiplication - Left to right
3. Addition & Subtraction - Left to right

Follow these steps EVERY TIME!

Practice Problem 1

Without Brackets

Calculate: 12 + 6 × 3

Think: Which operation first?

Practice Problem 1: Answer

12 + 6 × 3

Step 1: Multiply (6 × 3 = 18)
Step 2: Add (12 + 18 = 30)

Answer: 30

Practice Problem 2

With Brackets

Calculate: (12 + 6) × 3

How does this change the answer?

Practice Problem 2: Answer

(12 + 6) × 3

Step 1: Brackets (12 + 6 = 18)
Step 2: Multiply (18 × 3 = 54)

Answer: 54

12 + 6 × 3 = 30
(12 + 6) × 3 = 54

Big difference!

Practice Problem 3

Calculate: 50 - 20 ÷ 4

Step 1: Divide first
Step 2: Then subtract

What's the answer?

Practice Problem 3: Answer

50 - 20 ÷ 4

Step 1: Divide (20 ÷ 4 = 5)
Step 2: Subtract (50 - 5 = 45)

Answer: 45

Practice Problem 4

More Complex

Calculate: 8 × 5 + 15 ÷ 3

Practice Problem 4: Answer

8 × 5 + 15 ÷ 3

Step 1: Multiply (8 × 5 = 40)
Step 2: Divide (15 ÷ 3 = 5)
Step 3: Add (40 + 5 = 45)

Answer: 45

Practice Problem 5

With Brackets

Calculate: (8 + 2) × (15 - 5)

Two sets of brackets!

Practice Problem 5: Answer

(8 + 2) × (15 - 5)

Step 1: First brackets (8 + 2 = 10)
Step 2: Second brackets (15 - 5 = 10)
Step 3: Multiply (10 × 10 = 100)

Answer: 100

Word Problem!

Books in a Shop

Problem: A shop has 20 books. 15 more books arrive. They sell 5 packs of 3 books each. How many books remain?

How do we write this?

Word Problem: Solution

Write it: (20 + 15) - (5 × 3)

Step 1: First brackets (20 + 15 = 35)
Step 2: Second brackets (5 × 3 = 15)
Step 3: Subtract (35 - 15 = 20)

Answer: 20 books remain

Common Mistakes!

DON'T:

• Add before multiplying
• Ignore brackets
• Work from right to left
• Forget the order

DO:

• Follow BODMAS strictly
• Do brackets first
• Work left to right for equal operations
• Check your work!

Memory Tricks!

Remember BODMAS:

Buy Our Delicious Mangoes And Sugar

Or DMAS:

Do Maths After School

Quick Check! ✓

1. What does BODMAS stand for?

2. Calculate: 8 + 4 × 5

3. Calculate: (8 + 4) × 5

Quick Check: Answers

1. Brackets, Orders, Division, Multiplication, Addition, Subtraction

2. 8 + 4 × 5 = 8 + 20 = 28

3. (8 + 4) × 5 = 12 × 5 = 60

Summary of Topic 3!

What We've Learned

You can now handle ALL four operations!

Topic 3 Achievement!

You Can Now:

• Add numbers up to 9,999,999
• Subtract with regrouping
• Multiply large numbers
• Divide by two-digit divisors
• Use BODMAS for mixed operations
• Solve complex word problems

Excellent work!

Homework

1. 15 + 6 × 4 - 8 ÷ 2 = ?
2. (25 - 10) × 3 + 6 = ?
3. 100 - 40 ÷ 5 + 12 × 2 = ?
4. Word problem: A farmer has 50 chickens. He buys 3 groups of 12 chickens each. He sells 20 chickens. How many does he have now?

Show all working!

The BODMAS Rules!

1. Brackets first
2. Division & Multiplication (left to right)
3. Addition & Subtraction (left to right)

Follow these EVERY time!

Well Done!

You've completed Topic 3: Operations on Whole Numbers!

Next Topic: Patterns and Sequences

Keep practicing all four operations!