Order of Operations
Evaluate brackets, then exponents, then multiplication/division, then addition/subtraction (PEMDAS/BODMAS).
Key idea
Evaluate brackets, then exponents, then multiplication/division, then addition/subtraction (PEMDAS/BODMAS).
In depth
Without agreed rules, an expression could mean several things. Convention: brackets first, then exponents, then multiplication and division (left to right), then addition and subtraction (left to right).
Worked example
3 + 4 × 2 = 3 + 8 = 11, not 14. And (3 + 4) × 2 = 14.
Formula
Real-world uses
- Evaluating formulas in spreadsheets and calculators
- Reading expressions such as 3 + 4 × 2 correctly
Common mistake
Treating multiplication as always before division. They share the same level; go left to right.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Order of Operations?
Evaluate brackets, then exponents, then multiplication/division, then addition/subtraction (PEMDAS/BODMAS). It is a topic at the beginner level in Arithmetic & Number Sense.
What is the formula for Order of Operations?
The key formula is 2 + 3×4 = 14.
Where is Order of Operations used in real life?
Real-world examples: Evaluating formulas in spreadsheets and calculators; Reading expressions such as 3 + 4 × 2 correctly.
What should I learn before Order of Operations?
Make sure you are comfortable with Mental Math Strategies, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Order of Operations?
Treating multiplication as always before division. They share the same level; go left to right.
How can I practise Order of Operations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Order of Operations?
Move on to Word Problems next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Place Value – The value of a digit depends on its position: ones, tens, hundreds and so on.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.