BODMAS Lesson: Learn the Order of Operations

Lesson Overview

• What Does BODMAS Stand For?
• Why Do We Need BODMAS?
• Step-by-Step Guide to Solving BODMAS Problems
• Important Rule: Left to Right for D and M, A and S
• Working With More Than One Bracket
• Including Orders: Squares and Roots
• Common Mistakes in BODMAS and How to Avoid Them
• BODMAS in Real Life
• Sample Walkthrough Problems
• BODMAS with Word Problems

Have you ever seen a math problem with lots of different operations-like addition, subtraction, multiplication, and brackets-and wondered which part to solve first? That's where BODMAS comes in.

BODMAS is a rule that helps us solve complex math expressions in the correct order. Without it, people might get different answers for the same problem! In this lesson, we will learn what BODMAS stands for, how to apply it step-by-step, and why following the order of operations is so important in solving math problems accurately.

What Does BODMAS Stand For?

BODMAS is an acronym that tells us the correct order to solve a math expression:

You must follow this exact order to solve correctly.

Why Do We Need BODMAS?

Imagine two people solving this problem:
5 + 3 × 2

One person adds first:
(5 + 3) × 2 = 8 × 2 = 16

Another follows BODMAS and multiplies first:
5 + (3 × 2) = 5 + 6 = 11

The second answer is correct because multiplication comes before addition in BODMAS. This is why the rule is important-it makes sure we all get the same, correct result.

Take This Quiz:

Order of Operations Quiz Questions and Answers

Step-by-Step Guide to Solving BODMAS Problems

Let's break down how to solve a BODMAS expression in steps.

Example:
6 + (8 - 3) × 2

Step 1: Brackets
Solve the operation inside brackets first.
8 - 3 = 5

Now the expression becomes:
6 + 5 × 2

Step 2: Multiplication
Do multiplication before addition.
5 × 2 = 10

Now the expression becomes:
6 + 10

Step 3: Addition
6 + 10 = 16

Final Answer: 16

Important Rule: Left to Right for D and M, A and S

When you have both Division and Multiplication, or both Addition and Subtraction, do them from left to right.

Example:
20 ÷ 5 × 2

Step 1: Divide
20 ÷ 5 = 4

Step 2: Multiply
4 × 2 = 8

If you multiply first, you get a different and incorrect answer. So always follow left to right for D and M, and for A and S.

Working With More Than One Bracket

Some expressions have nested brackets-one bracket inside another.

Types of brackets:

• ( ) = Parentheses
  
• = Square brackets
  
• { } = Curly brackets
  

When solving, start from the innermost bracket and move outward.

Example:
8 + {3 × [2 + (1 + 1)]}

Step 1: (1 + 1) = 2
Now: 8 + {3 × [2 + 2]}

Step 2: [2 + 2] = 4
Now: 8 + {3 × 4}

Step 3: 3 × 4 = 12
Now: 8 + 12 = 20

Answer: 20

Including Orders: Squares and Roots

Orders include:

• Powers (like 2 squared = 2 × 2 = 4)
  
• Square roots (√)
  

If there are orders in the expression, solve them after brackets and before division.

Example:
3 + (2 × 2)²

Step 1: Brackets
2 × 2 = 4
Now: 3 + 4²

Step 2: Order
4² = 16
Now: 3 + 16 = 19

Answer: 19

Common Mistakes in BODMAS and How to Avoid Them

Take your time and double-check the order in each problem.

Take This Quiz:

BODMAS Quiz Questions And Answers

BODMAS in Real Life

You may not realize it, but BODMAS is used in many real-world situations:

• Shopping: Calculating discounts or total costs
  
• Cooking: Changing recipes (e.g., doubling ingredients)
  
• Construction: Measuring and dividing space
  
• Science experiments: Solving equations or converting units
  

Using BODMAS helps make sure calculations are accurate and consistent.

Sample Walkthrough Problems

Let's solve a few problems step-by-step to apply BODMAS.

Problem 1:
5 × (6 + 4) ÷ 2 - 3

Step 1: Brackets
6 + 4 = 10
Expression becomes: 5 × 10 ÷ 2 - 3

Step 2: Multiply
5 × 10 = 50
Now: 50 ÷ 2 - 3

Step 3: Divide
50 ÷ 2 = 25
Now: 25 - 3 = 22

Problem 2:
(9 - 4) + 6 × 2

Step 1: Brackets
9 - 4 = 5
Now: 5 + 6 × 2

Step 2: Multiply
6 × 2 = 12
Now: 5 + 12 = 17

Problem 3:
15 ÷ 3 + 2 × 4

Step 1: Divide
15 ÷ 3 = 5
Now: 5 + 2 × 4

Step 2: Multiply
2 × 4 = 8
Now: 5 + 8 = 13

BODMAS with Word Problems

You can also apply BODMAS in story or word problems. Here's an example:

"A basket has 3 apples. Each apple costs 5 dollars. A discount of 6 dollars is given on the total. What is the final cost?"

Let's write the equation:
3 × 5 - 6

Step 1: Multiply
3 × 5 = 15

Step 2: Subtract
15 - 6 = 9

Answer: 9 dollars

Word problems often mix different operations, so using BODMAS ensures you solve them in the right order.