Order of Operations: Why 3 + 4 × 2 Is Not 14

19 September 2026 · by Larry

The question is 3 + 4 × 2. She reads it the way she reads a sentence, from left to right: 3 add 4 is 7, 7 times 2 is 14. She writes 14, checks it, and is sure of it.

The answer is 11. The multiplying is done first — 4 × 2 is 8 — and then the adding: 3 + 8 is 11. Her adding was right and her multiplying was right. What went wrong was the order she did them in, and nothing in the question told her which order to use. She was simply expected to know.

That is why this topic feels unfair to children. The sums are easy. The marks go on which part comes first, and a child with a shaky — or slightly wrong — version of that rule loses marks on questions they could otherwise do in their sleep.

Why there has to be a rule at all

Without an agreed order, 3 + 4 × 2 has two answers, 14 and 11, and both follow sensibly from what was written. Maths cannot live with that, so there is a convention everyone follows, and once a child sees that it is a convention — an agreement, not a trick — it tends to stick better.

It is also worth knowing that a cheap four-function calculator, the kind that works out each step as you press it, will usually show 14 for that same sum. So a child who checks on one can "prove" the wrong answer. The MOE primary mathematics syllabus lists order of operations and the use of brackets under Primary 5, and it says both are done without calculator. This is a paper-and-pencil rule.

The rule in plain words:

• Brackets first. Whatever is inside ( ) is worked out before anything else.
• Then multiply and divide, working from left to right.
• Then add and subtract, working from left to right.

The words "left to right" in the second and third lines are the part that most often goes missing. More on that below.

The slips, and how to tell them apart

1. Going left to right all the way through. This is the opening example. The child treats the sum like a sentence and works through it in reading order, so 3 + 4 × 2 becomes 14. It is the most natural mistake there is, because nearly every sum they met before this topic could be done left to right. The tell is an answer that is exactly what you get by starting at the beginning and ploughing on.

2. Reading the memory word as a strict order. Some children learn a word such as BODMAS to remember the rule — Brackets, Orders, Division, Multiplication, Addition, Subtraction. The trouble is that the letters come in a line, so the child concludes that within each pair, one always goes first. Where it costs marks is when a child adds before subtracting, or multiplies before dividing, because they have decided that is the order. It is not. Multiply and divide are equal partners, and so are add and subtract; within each pair you go left to right.

So 20 − 5 + 3 is 15 + 3, which is 18. A child who adds first does 5 + 3 = 8, then 20 − 8 = 12. And 12 ÷ 3 × 2 is 4 × 2, which is 8; a child who multiplies first does 3 × 2 = 6, then 12 ÷ 6 = 2. These children have usually learned the rule quite carefully — just the wrong version of it — and the tell is that they are confidently wrong on every question of this shape.

3. Brackets that come undone. In 30 − (8 + 2), the bracket says: take away the whole 10. The answer is 20. A child who lets the bracket go works 30 − 8 = 22, then adds the 2 to get 24. The bracket was there precisely to stop the 2 being added back on, and it got ignored.

4. Losing part of the sum on the way down. Longer questions need more than one step, and each step means copying the rest of the line down. Take 40 − 6 × 5 + 2. Done properly: 6 × 5 is 30, so the line becomes 40 − 30 + 2, which is 10 + 2, which is 12. A child who gets the first step right can still write 40 − 30 = 10 and stop, because the "+ 2" fell off when they rewrote the line. The rule was fine. The copying was not.

5. The running chain of equals signs. Some children write the whole thing in one line: 3 + 4 = 7 × 2 = 14. Each equals sign in that chain is saying something untrue — 3 + 4 is not 14 — and the habit also pushes them into left-to-right order, because they can only ever carry on from the last number they wrote. Where the working is marked as well as the answer, a line of untrue statements can cost marks even when the final number happens to be right. It is closely related to the working-shown problems in the answer was right and the marks still went.

A five-question check at the kitchen table

Write these on paper and let them work alone. Do not react until all five are done — a face at question one changes how questions two to five get answered.

• 3 + 4 × 2 — the answer is 11. If they write 14, they are going left to right (slip 1).
• 20 − 5 + 3 — the answer is 18. If they write 12, they think adding comes before subtracting (slip 2).
• 12 ÷ 3 × 2 — the answer is 8. If they write 2, they think multiplying comes before dividing (slip 2).
• 30 − (8 + 2) — the answer is 20. If they write 24, the bracket came undone (slip 3).
• 40 − 6 × 5 + 2 — the answer is 12. An answer of 172 is left to right; 8 is adding before subtracting; 10 is the lost "+ 2" (slip 4). Look at how the working is laid out too (slip 5).

The last question is the useful one, because the wrong answer itself tells you which slip it was. Most children turn out to have one main slip, not all five, and the fix for each is different.

What actually helps at home

One step per line. Get them to underline the part they will do first, work it out, and then rewrite the whole line underneath with that part replaced by its answer. So 40 − 6 × 5 + 2 becomes 40 − 30 + 2 on the next line, then 10 + 2, then 12. It looks slow, but it stops slip 4, ends the running equals signs of slip 5, and shows you exactly where things went wrong.

Tie the rule to a story. "Mum bought 3 packets of 4 sweets, and there were 5 loose sweets in the bag. How many sweets?" Nobody adds 5 + 3 first — you count the packets, then add the loose ones. Written as a sum, that is 5 + 3 × 4 = 17, and the multiplying comes first because a multiplication is a set of groups that has to be counted before anything is added to it. A child who has made that connection once finds the rule much less arbitrary. It is the same reading-the-story skill that matters in word problems.

Say "equal partners" out loud. For slip 2, drop the letter-by-letter reading of the memory word. Tell them: multiply and divide are partners; add and subtract are partners; when partners meet, go left to right. Then do three or four sums like 20 − 5 + 3 and 12 ÷ 3 × 2 together, saying the rule each time, until it comes out without prompting.

Treat a bracket as a box. For slip 3, ask them to draw a circle round the bracketed part and work that out first, writing the answer above it. 30 − (8 + 2) becomes 30 − 10 before anything else happens. A useful follow-up is to let them put brackets in: in 3 + 4 × 2, writing 3 + (4 × 2) does not change the answer, because the bracket goes round the part that would come first anyway. When they are unsure, adding their own brackets to show the order is a safe habit.

Ask "which part did you do first, and why?" "The times, because times comes before plus" is a secure answer. A finger pointing at the left-hand end is slip 1.

What does not help

• Drilling the memory word on its own. Reciting it letter by letter is exactly what produces slip 2. If a memory word is used at all, it needs "partners, left to right" attached to it every time.
• A calculator. A basic one may work left to right and give the wrong answer, and the syllabus treats this topic as calculator-free anyway.
• Only practising sums with brackets. Brackets tell the child what to do. The marks are lost on sums without them, where the child has to know.
• "Just be careful." Every one of these slips has a specific cause. A child told to be careful will be careful in the same wrong order. The careless mistakes piece goes into why that advice rarely lands.

Where it turns up again

Order of operations does not stay a topic of its own for long. It sits underneath longer word problems, where a child writes one number sentence for a two-step story, and later underneath algebra, where the same rules decide what an expression means. A child who quietly goes left to right keeps losing marks on questions that look as if they are about something else. That is part of why the jump in the upper primary years can feel sudden — see what actually changes from P4 to P5.

Where a screen fits, honestly

StudyLab's Primary 5 topic Order of Operations gives quick sums in the shape 3 + 4 × 2, with a hint that multiplying comes before adding. That is useful for slip 1, because a child gets a lot of repetitions and immediate feedback on exactly that mistake. It does not cover brackets, the left-to-right partners of slip 2, or the written working of slips 4 and 5 — the answer is typed as a single number, so nobody sees the lines in between. Those are for paper, and for you sitting beside them asking "which part did you do first?"

The short version

• Brackets first, then multiply and divide, then add and subtract.
• Within each pair, go left to right — division does not always come before multiplication, and addition does not always come before subtraction.
• Most children have one main slip; 40 − 6 × 5 + 2 tells you which (the answer is 12).
• One step per line, rewriting the whole line each time.
• This is a no-calculator topic; a basic calculator can give the left-to-right answer.
• Ask "which part did you do first?" — the answer tells you more than the mark.