11+ Order of Operations: BODMAS Questions and Answers

A calculation can contain all the right numbers and still give the wrong answer if you combine them in the wrong order. Order of operations is the shared convention that makes an expression mean the same thing to different readers. It is especially useful when checking algebra, prices or a line of working in a longer problem.

These original questions support preparation for exams taken in 2027. They are not official school papers. Topic coverage and question formats vary: check your target school’s current information. Try the questions on paper before opening each answer.

Read the expression before calculating

BODMAS and BIDMAS are reminders of the same ordering convention. The O means orders and the I means indices: powers such as a square. The important detail is that the four operations do not have four separate priority levels. Multiplication and division share a level; addition and subtraction share another.

Do not treat the letters as a rule that division must always happen before multiplication, or addition before subtraction. At a shared level, position decides the next operation. Also, left to right does not mean ignoring priority and completing every operation as you meet it.

Worked example: two equal-priority operations

Consider 42 ÷ 7 × 3. Divide first because it is the leftmost operation at that level: 42 ÷ 7 = 6, then 6 × 3 = 18. If you multiply 7 × 3 first, you have silently changed the expression to 42 ÷ (7 × 3). That is a different calculation.

Worked example: preserve the rest of the line

For 19 + 4 × (8 − 5), first replace only the bracket with its value: 19 + 4 × 3. Next replace the product: 19 + 12. Finally add to obtain 31. Writing a complete new line after each step helps you keep the initial 19 and prevents an unfinished intermediate answer becoming your final one.

Compare this with (19 + 4) × (8 − 5). The first bracket is now 23 and the second is 3, giving 69. The numbers have stayed the same, but the grouping has changed. Brackets communicate meaning; they are not decoration.

A short extension: squares

For 6² − 12 ÷ 3, square 6 to make 36. Divide 12 by 3 to make 4, then subtract: 36 − 4 = 32. Squaring does not mean doubling, so 6² is not 12. Keep this extension separate if you are still building confidence with the four basic operations.

Eight original questions

Check the method, not only the total

• Underline the first operation before doing any arithmetic.
• Change one part of the expression at a time and copy everything else accurately.
• If two answers disagree, locate the first different line rather than repeating the whole question faster.

Next, use this convention in algebra basics. For choosing an operation from a story, work through our multi-step word problems. Return to the maths hub for the wider learning sequence.

Curriculum context: the Department for Education maths programme includes order of operations in Year 6. This is a learning reference, not a single national 11-plus syllabus. Sources and answers checked 24 October 2026.