Order of Operations Explained: BIDMAS, BODMAS, PEMDAS and BEDMAS

By the Success Tutoring team · 5 October 2026

What is 3 + 4 × 2? If you work left to right you get 14, but the correct answer is 11. Mathematicians everywhere agree on an order for doing calculations, so that a question written down has only one right answer. This order is called the order of operations, and children learn it with a memory word such as BIDMAS, BODMAS, PEMDAS or BEDMAS. They are all the same rule with different names.

The order, in plain words

1. Brackets (also called parentheses) first.
2. Powers and roots, such as 3² or √16. These are called indices, orders or exponents.
3. Multiplication and division, working from left to right.
4. Addition and subtraction, working from left to right.

BIDMAS, BODMAS, PEMDAS and BEDMAS

Different countries and schools use different memory words. They look different, but they describe exactly the same order:

Use whichever one your child's school uses, so they hear the same word at home and in class.

The big catch: some steps are a tie

This is the part most people get wrong. Multiplication and division have equal priority, and so do addition and subtraction. When they appear together, you work from left to right. The memory words hide this, because one letter has to come first.

• 12 ÷ 3 × 2: left to right, 12 ÷ 3 = 4, then 4 × 2 = 8. If you multiply first because M comes before D in PEMDAS, you get 12 ÷ 6 = 2, which is wrong.
• 10 − 4 + 3: left to right, 10 − 4 = 6, then 6 + 3 = 9. Adding first gives 10 − 7 = 3, which is wrong.

A helpful way to picture it is as three levels rather than six letters:

Worked examples

Encourage your child to rewrite the whole calculation after each step, doing one operation at a time. It feels slow, but it prevents almost every mistake.

Notice how the brackets change the answer in the first two rows: the same numbers give 17 or 32. That's why brackets exist. They let you say “do this part first”.

Common mistakes

• Working left to right for everything. 5 + 3 × 4 is not 32. Multiplication comes before addition.
• Always multiplying before dividing. In 12 ÷ 3 × 2, divide first because it comes first. The answer is 8.
• Always adding before subtracting. In 10 − 4 + 3, subtract first. The answer is 9.
• Squaring the wrong thing. In 2 × 3², only the 3 is squared, giving 18. To square the whole of 2 × 3 you need brackets: (2 × 3)² = 36.
• Trusting a simple calculator. Many basic calculators work strictly left to right, so typing 5 + 3 × 4 can show 32. Scientific calculators follow the order of operations. Try both with your child, which makes a great discussion.

What about those viral puzzles?

Online puzzles like 6 ÷ 2(1 + 2) cause endless arguments. Working strictly left to right gives 9, but some people treat 2(1 + 2) as one unit and get 1. The real problem is that the question is written ambiguously on purpose. In proper maths you would add brackets to make the meaning clear, which is a great lesson in itself.

Games to practise at home

• Add the brackets: write 2 + 3 × 4 = 20 and ask your child where brackets must go to make it true. (Answer: (2 + 3) × 4.) Then try 12 − 4 ÷ 2 = 4, which needs (12 − 4) ÷ 2.
• Make the target: roll three dice and try to make a target number using any operations. With 2, 3 and 4, you can make 10 as 2 × 3 + 4 or 4 × 3 − 2.
• Spot the error: work out a few questions yourself, including one deliberate mistake, and let your child mark them.

For printable practice, try the order of operations worksheet. Squared numbers turn up in many of these questions, so our guide to square and cube numbers is a useful next step.

When do children learn the order of operations?

Most children meet the order of operations with brackets, multiplication, division, addition and subtraction around Year 5 to Year 6. Powers are added in the last year of primary or early secondary school, and the rules become essential in algebra.

Frequently asked questions