It is 34, not 10. Division and multiplication are done before addition and subtraction, so you do 60 ÷ 2 = 30 first, then add 4 to get 34. Reading strictly left to right and grouping the last two numbers as 2 + 4 = 6 gives the wrong calculation 60 ÷ 6 = 10. The division is stronger than the addition, so it goes first regardless of the order the numbers are written.

Do you always work a calculation from left to right?

No. You work left to right only as a tie-breaker between operations of equal strength. The priority is brackets first, then powers, then multiply and divide together, then add and subtract together. So in 35 − 19 ÷ 2 you do the division first, 19 ÷ 2 = 9.5, then 35 − 9.5 = 25.5. Left to right only decides the order when two operations are at the same level, for example between a × and a ÷, or between a + and a −.

Why do brackets have to be finished first?

A bracket is a single value waiting to be worked out; nothing outside it can act until it has been collapsed to one number. In 3 × (4 + 2) the bracket is 4 + 2 = 6, so the calculation is 3 × 6 = 18. Treating it as 3 × 4 + 2 = 14 reaches into the bracket before it is finished, which breaks the rule. Always evaluate what is inside the brackets to a single number first, then carry on.

GCSE Maths Foundation · AQA · Order of operations & negatives

Order of operations: × and ÷ before + and −, brackets first

A calculation read strictly left to right goes wrong the moment a × or ÷ sits next to a + or −. Students compute $60 \div 2 + 4$ as $60 \div 6 = 10$ , grouping the last two numbers, when division is stronger than addition and must go first for 34. The same slip reaches into a bracket before it is finished, turning $3 \times (4 + 2)$ into $3 \times 4 + 2 = 14$ instead of $3 \times 6 = 18$ .

The thirty-second fix: do brackets first, then powers, then multiply and divide together, then add and subtract together — and only use left-to-right to break ties between operations of equal strength. So $60 \div 2 + 4 = 30 + 4 = 34$ and $3 \times (4 + 2) = 3 \times 6 = 18$ .

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How to spot it in your own work

You worked $60 \div 2 + 4$ left to right as $60 \div 6 = 10$ , grouping the last two numbers, when the division goes first for 34.
You did the + or − before the × or ÷, e.g. $35 - 19 \div 2$ taken as $16 \div 2 = 8$ rather than $35 - 9.5 = 25.5$ .
You reached into a bracket before finishing it, writing $3 \times (4 + 2) = 3 \times 4 + 2 = 14$ instead of $3 \times 6 = 18$ .
You dropped a bracket on a subtraction, e.g. $21 - (15 - 4)$ taken as $21 - 15 - 4 = 2$ rather than $21 - 11 = 10$ .

An exam question that triggers it

Here is a canonical AQA Foundation trigger (non-calculator paper, work out the value):

Work out

$60 \div 2 + 4$

The misconception is to read it straight across — sixty, divide, two, add, four — and group the last two numbers as $2 + 4 = 6$ , giving $60 \div 6 = 10$ . But division is stronger than addition, so it does not wait its turn.

Do the division first: $60 \div 2 = 30$ , then add the 4 to get 34. The order the symbols are written in does not change which operation is the stronger one.

Why students fall for this

Left to right is how we read words, so it feels like the natural way to read a sum too. For a string of all-equal operations it even works — but the moment a stronger operation (× or ÷) sits to the left of a weaker one (+ or −), reading across does the weaker one too early. The operations are not equal: multiply and divide outrank add and subtract, whatever order they appear in.

Brackets get the mirror-image slip. A bracket is a single value that has not been worked out yet, so nothing outside it may act until it has collapsed to one number. Students reach in early — $3 \times (4 + 2)$ becomes $3 \times 4 + 2 = 14$ — when the bracket must be finished first: $4 + 2 = 6$ , then $3 \times 6 = 18$ . The same care matters for a bracketed subtraction, where $21 - (15 - 4)$ is $21 - 11 = 10$ , not $21 - 15 - 4 = 2$ .

AQA Foundation papers exploit both directly: a mixed × ÷ + − string where the stronger operation is written second, and a bracketed product or difference where finishing the bracket first changes the answer.

Worked example — a mixed string. Work out $35 - 19 \div 2$ .

Division outranks subtraction, so do it first, then subtract:

35 - 19 \div 2 = 35 - 9.5 = 25.5

The trap is to subtract first — $35 - 19 = 16$ , then $16 \div 2 = 8$ — which does the weaker operation before the stronger one. Multiply and divide come first.

The fix: Brackets, then powers, then × and ÷, then + and − — left-to-right only to break ties

Finish every bracket first. A bracket is one value waiting to be found; collapse it to a single number before anything outside it acts. $3 \times (4 + 2) = 3 \times 6 = 18$ , never $3 \times 4 + 2$ .

Then powers. Square and other indices come after brackets but before the four operations.

Then multiply and divide, together. These are stronger than + and −, so they go next regardless of where they sit in the line: $60 \div 2 + 4 = 30 + 4 = 34$ .

Then add and subtract, together — left to right only as a tie-breaker. When two operations are at the same level (× with ÷, or + with −), and only then, you work them in the order written.

Worked example

Work out $3 \times (4 + 2)$ and $21 - (15 - 4)$ . These are the bracket traps: nothing outside a bracket acts until the bracket is one number.

Finish the bracket in the product. $4 + 2 = 6$ , so the calculation becomes $3 \times 6$ .
Now multiply.
$3 \times (4 + 2) = 3 \times 6 = 18$
The trap answer, $3 \times 4 + 2 = 14$ , reaches into the bracket before it is done.
Finish the bracket in the difference. $15 - 4 = 11$ , so the calculation becomes $21 - 11$ .
Now subtract.
$21 - (15 - 4) = 21 - 11 = 10$
Dropping the bracket gives $21 - 15 - 4 = 2$ , a different answer — the bracket protects the difference until it is found.

The same priority settles the opening trigger: $60 \div 2 + 4 = 30 + 4 = 34$ , because the division is stronger than the addition and so goes first — not the $60 \div 6 = 10$ that reading left to right produces.

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Common questions

What is $60 \div 2 + 4$ ?: It is 34, not 10. Division and multiplication are done before addition and subtraction, so you do $60 \div 2 = 30$ first, then add 4 to get 34. Reading strictly left to right and grouping the last two numbers as $2 + 4 = 6$ gives the wrong calculation $60 \div 6 = 10$ . The division is stronger than the addition, so it goes first regardless of the order the numbers are written.
Do you always work a calculation from left to right?: No. You work left to right only as a tie-breaker between operations of equal strength. The priority is brackets first, then powers, then multiply and divide together, then add and subtract together. So in $35 - 19 \div 2$ you do the division first, $19 \div 2 = 9.5$ , then $35 - 9.5 = 25.5$ . Left to right only decides the order when two operations are at the same level, for example between a × and a ÷, or between a + and a −.
Why do brackets have to be finished first?: A bracket is a single value waiting to be worked out; nothing outside it can act until it has been collapsed to one number. In $3 \times (4 + 2)$ the bracket is $4 + 2 = 6$ , so the calculation is $3 \times 6 = 18$ . Treating it as $3 \times 4 + 2 = 14$ reaches into the bracket before it is finished, which breaks the rule. Always evaluate what is inside the brackets to a single number first, then carry on.

Related misconceptions

Ordering and signs of negative numbersThe neighbouring directed-number skill: on a number line further left is smaller, so −7 < −5, and the sign rules hold, so −3 × 3 = −9.
Squaring a negative numberWhere order of operations meets signs: the bracket decides, so (−4)² = 16 but −4² = −16, because the square only reaches the 4.

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