Year 10 revision: Understanding the order of operations (BODMAS)
Back to tutorialsUnderstanding the order of operations is absolutely crucial for correctly solving mathematical expressions. This guide will break down BODMAS - the mnemonic you'll use to remember the correct sequence.
Work through the sections in order, then try the linked Year 10 skill quizzes after each section.
What is BODMAS?
BODMAS is an acronym that stands for:
- Brackets (or parentheses)
- Orders (or powers and surds)
- Division
- Multiplication
- Addition
- Subtraction
Essentially, you must perform operations within the brackets first, then exponents, followed by division and multiplication (working from left to right), and finally addition and subtraction (again, working from left to right).
Skill quiz: Follow the order of operations
Identify brackets, powers and the operations to complete first.
Let’s break it down with examples
Example 1: 2 + 3 x 4
Step 1: Brackets - None in this example. Step 2: Orders - None in this example. Step 3: Division & Multiplication (left to right) - 3 x 4 = 12 Step 4: Addition - 2 + 12 = 14
Therefore, 2 + 3 x 4 = 14
Example 2: (5 + 2) x 3 - 6
Step 1: Brackets - (5 + 2) = 7 Step 2: Orders - None in this example. Step 3: Multiplication - 7 x 3 = 21 Step 4: Subtraction - 21 - 6 = 15
Therefore, (5 + 2) x 3 - 6 = 15
Example 3: 10 - 22 + 5 x 1
Step 1: Orders - 22 = 4 Step 2: Multiplication - 5 x 1 = 5 Step 3: Subtraction - 10 - 4 = 6 Step 4: Addition - 6 + 5 = 11
Therefore, 10 - 22 + 5 x 1 = 11
Exercise
Skill quizzes: Evaluate expressions step by step
Practise the full order of operations, then include expressions with powers.
Key reminders
- Always work from left to right within each operation.
- Don’t be tempted to skip steps! Careful attention to detail is key.
- Practice, practice, practice! The more you work through examples, the more comfortable you'll become with BODMAS.
Skill quiz: Work carefully from left to right
Work from left to right within multiplication and division, and within addition and subtraction. Write each intermediate step.