Order of Operations with Real-Life Examples (Simple Guide for Kids)
I've lost count of how many times a student has shown me two different answers for the exact same sum, both worked out carefully, both wrong in different ways. It usually comes down to one thing: the order the operations were done in.
Maths has a set order for solving a question with more than one operation in it. Once a child knows that order, mixed sums stop being a guessing game. The best part is that this rule shows up everywhere outside the classroom too — shopping trips, sports scores, recipes, all of it.
Why the order actually matters
Take a simple sum: 6 + 2 × 3. Add first and you get 8 × 3 = 24. Multiply first and you get 6 + 6 = 12. Only one of those is correct, and maths needs everyone in the world to agree on which one.
The agreed order is: brackets first, then powers (small numbers written above a number, like squaring), then multiplication and division, then addition and subtraction. Multiplication and division are done together, left to right. Addition and subtraction are done together, left to right, after that.
So 6 + 2 × 3 is 6 + 6, which is 12. You may already know this rule by the name BODMAS or PEMDAS — different names, same order.
Real-life example: the shopping trip
Imagine you buy 3 packs of pencils at £2 each, and one ruler at £1. You don't add the ruler and one pencil pack together first — you work out the cost of all the pencils, then add the ruler. That's 3 × 2 + 1 = 6 + 1 = £7.
If someone added 2 + 1 first by mistake, they'd get 3 × 3 = £9, which is wrong. The shop till doesn't make that mistake, and neither should we.
Real-life example: the restaurant bill
Two meals cost £9 each, you share one dessert for £4, and you have a £2 voucher off the total. The bill is 2 × 9 + 4 − 2. Multiply first: 18. Then add and subtract left to right: 18 + 4 = 22, then 22 − 2 = 20. The bill is £20.
Real-life example: sports scoring
In rugby, a try is worth 5 points and a conversion is worth 2 points. A team scores 3 tries and 2 conversions. The score is 3 × 5 + 2 × 2. Do both multiplications first — 15 and 4 — then add them: 15 + 4 = 19 points. You'd never add a try to a conversion before multiplying by how many of each there were, and the order of operations is just the maths version of that same common sense.
Real-life example: sharing cookies (brackets)
You bake 12 cookies. You keep 4 for yourself, and share the rest equally between 4 friends. That's (12 − 4) ÷ 4. Brackets go first: 12 − 4 = 8. Then divide: 8 ÷ 4 = 2. Each friend gets 2 cookies.
Without the brackets, 12 − 4 ÷ 4 would mean divide first: 4 ÷ 4 = 1, then 12 − 1 = 11 — a completely different, and wrong, answer for this situation. Brackets are how we tell maths "do this bit together, as one group, first."
Real-life example: a square garden bed
A square garden bed has sides of 4 metres. You're building 2 identical beds and want the total area. That's 2 × 4². Powers come before multiplication, so work out 4² first: 4 × 4 = 16. Then multiply: 2 × 16 = 32 square metres.
Practice questions
Cover the answers and try these yourself first.
- 6 + 2 × 3 = ? Answer: 12
- (5 + 3) × 2 = ? Answer: 16
- 20 ÷ 4 + 3 × 2 = ? Answer: 11
- 10 − 2 × 3 = ? Answer: 4
- 3² + 4 = ? Answer: 13
Common mistakes I see in the classroom
The biggest one is solving strictly left to right, ignoring the rule entirely — treating 6 + 2 × 3 as (6 + 2) × 3. It's an easy habit to fall into because reading left to right feels natural everywhere else.
The second is forgetting that multiplication and division are equal partners, done left to right in the order they appear — not multiplication always before division. The same goes for addition and subtraction.
The third is rushing past brackets without solving what's inside them completely before moving on to the rest of the sum.
Tips for parents
You don't need to remember the name of the rule to help. Just ask your child to point at the sum and say out loud what they're doing first, second, and third. If they jump straight to adding without checking for multiplication or brackets, gently ask, "Is there anything we should do before that?"
Tips for teachers
I've found it helps to have students physically circle the operation they're doing first in a different colour before writing anything down. It slows the rush to solve and makes the order visible on the page, which matters more than it sounds for younger students.
How step-by-step learning tools help
A mixed operations question is exactly where children benefit most from seeing every step written out, rather than just the final number. A step-by-step maths tool can show which operation is done first and why, work through unlimited practice questions, and let a child repeat a tricky example as many times as they need until the order clicks.
Frequently asked questions
Is the order of operations the same as BODMAS? Yes. BODMAS and PEMDAS are two names, used in different countries, for exactly the same order: brackets, powers, multiplication and division, then addition and subtraction.
Why does multiplication come before addition? It isn't an arbitrary rule — it's an agreement that lets everyone read the same sum and get the same answer, in the same way road signs use the same colours everywhere so drivers don't get confused.
What age should children learn this? Most children in the UK meet the order of operations informally around age 8 to 9, and it's formally named and tested a little later, usually around age 10 to 11.
Do division and multiplication always happen in a fixed order? No — whichever one appears first when reading left to right is done first, since they carry equal weight.
What's the easiest way to check an answer? Rewrite the sum with brackets around the part you did first, and read it back — if it says what you actually meant to calculate, your order was correct.
One Rule, Many Everyday Uses
The order of operations isn't a school-only rule that disappears once the test is over. It's the same logic behind working out a bill, a sports score, or a fair share of cookies. Once a child sees it in those everyday moments, the classroom version stops feeling abstract, and starts feeling like something they already half-knew.