Topics · Primary Maths · Order of Operations
Order of operations: which part to do first
A calculation with more than one operation has exactly one right answer, and the order is agreed rather than obvious. Brackets first, then multiply and divide, then add and subtract.
- 147 exam papers analysed
- appears in 62% of P6 Maths papers
- ~3 min read
01 Why an order is needed at all
2 + 3 × 4 could be 20 if you work left to right, or 14 if you multiply first. Both are reasonable readings, so mathematics fixes one of them by agreement: 14.
Without a fixed order, the same written calculation would mean different things to different people, and no answer could be marked right or wrong.
02 The order
Four levels, worked from the top down. Anything at the same level is done left to right.
- Brackets first. Everything inside them, before anything outside.
- Then multiply and divide, left to right, taking whichever comes first.
- Then add and subtract, left to right, same rule.
- Within a level, always left to right. 12 ÷ 3 × 2 is (12 ÷ 3) × 2 = 8, not 12 ÷ 6 = 2.
03 The two that catch people
Multiply does not beat divide. They sit at the same level, so 12 ÷ 3 × 2 is worked left to right: 4 × 2 = 8. Doing the multiplication first gives 2, and it is wrong.
Add does not beat subtract, for the same reason. 10 − 4 + 3 is (10 − 4) + 3 = 9, not 10 − 7 = 3.
Rhymes that list the operations as though each beat the next cause both of these errors. The four levels are what matter, not the six letters.
04 Working it down
Write one line per step, changing only the part you worked out. It is slower to start and much faster to check, and a marker can follow it.
Rushing to a single line is where terms get dropped, and there are no marks for having done it in your head.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- operationsayop-uh-RAY-shuhnmore than oneoperations
One of add, subtract, multiply or divide.
- bracketsmore than onebrackets
The curved marks ( ) showing which part to work out first.
- expressionsayik-SPRESH-uhnmore than oneexpressions
A calculation written out, like 2 + 3 x 4.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P5
Calculations with brackets and two operations, and working left to right within a level.
Practise P5 Order of Operations — 10 questions →47% of P5 papers
- P6
Longer expressions, brackets inside brackets, and order of operations inside word problems.
Practise P6 Order of Operations — 10 questions →62% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“12 ÷ 3 × 2 = 2, because multiplication comes first.”
It does not. Multiply and divide are the same level, so work left to right: 12 ÷ 3 = 4, then 4 × 2 = 8.
“10 − 4 + 3 = 3, because addition comes before subtraction.”
Same level again, so left to right: 10 − 4 = 6, then 6 + 3 = 9.
“2 + 3 × 4 = 20.”
Multiplication is done before addition, so it is 2 + 12 = 14. Left to right only applies within a level.
“There are no brackets, so the order does not matter.”
It matters most when there are none — brackets are the tool for overriding the order, and without them the order is doing all the work.
“I did it all in one line to save time.”
One line per step costs seconds and catches the dropped term. There is no mark for speed.
Now try it
20 questions across 2 levels, marked as you go with the working shown.