Concept 9 of 10
Brackets First: The Order of Operations
Today's big idea
Multiply and divide before you add and subtract, and brackets outrank both.
4 + 5 x 2 is 14, not 18. Adding first is the rung below multiplying.
How it works
👀 What's going on?
Two people work out 4 + 5 x 2. One gets 18, the other gets 14. Both did real arithmetic, and only one is right. When a sum has more than one sign, the order you work in changes the answer, so everybody has to agree on one order.
💡 Here's the trick
Look at the ladder above. Brackets come first, then multiply and divide, then add and subtract. So in 4 + 5 x 2 the multiplying happens first: 5 x 2 is 10, and 4 + 10 is 14. The 18 came from adding first, which is the rung below. Brackets are how you overrule the ladder. Writing (4 + 5) x 2 forces the addition to the front and does give 18. Same digits, same signs, different answer, because the brackets changed the order.
🪄 How to do it
- 1.Work out anything inside brackets first, as the ladder above shows.
- 2.Then do every multiplication and division, working left to right.
- 3.Then do every addition and subtraction, working left to right.
✍️ Try it
Work out 20 - 3 x 4. Then work out (20 - 3) x 4.
In the first, multiply before you subtract: 3 x 4 is 12, and 20 - 12 is 8. In the second the brackets go first: 20 - 3 is 17, and 17 x 4 is 68. One pair of brackets moved the answer from 8 to 68.
⚠️ Watch out
You might be thinking you should always work left to right, the way you read. That only applies inside a rung. In 12 - 2 x 5, reading left to right gives 50, but multiplying first gives 12 - 10 = 2. Left to right settles ties, it does not beat the ladder.
🌟 Why this matters
A shop bill works this way without anyone writing brackets. Three samosas at 12 rupees plus one drink at 20 is 3 x 12 + 20, and nobody adds the 12 and the 20 first. Calculators and spreadsheets follow the same ladder.
Exam tip: Circle the multiplication and division before you start, so the order is decided before you calculate.
See it in action
⚡ Time to play!
WHICH GOES FIRST?
4 + 5 × 2
Two different signs, so the order decides the answer. Tap the part you would do first.
Quick check
✅ VERIFICATION
What is 6 + 4 x 3?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Find the Rule
4→28, 5→35, so the rule is × 7.