BODMAS questions with answers: 30 questions for Class 5, 6 and 7 (and Year 6 to 8) with worked solutions, the rule explained properly, the "division before multiplication" myth, and a free PDF

"BODMAS questions with answers" is typed in India by Class 5 to 7 parents and in the UK by Year 6 to 8 parents, usually with a specific worksheet in hand and a disagreement in the house about whether 8 − 2 × 3 is 18 or 2. (It is 2.) This page explains the rule the way it is actually meant, which is not quite what the letters suggest, then gives 30 questions in three levels with ten worked in full and all thirty answered, and a free PDF of the set.

Download the 30 questions with answers (PDF) (A4, questions on page 1, answers with working on page 2, free).

The rule, stated properly

BODMAS is four steps, not six:

1. Brackets: work out anything inside brackets first. Nested brackets: innermost first.
2. Orders: powers (indices, exponents) and roots. 3² = 9 before anything is multiplied by it.
3. Division and Multiplication: equal rank. Work them left to right in the order they appear.
4. Addition and Subtraction: equal rank. Work them left to right in the order they appear.

The letters put D before M and A before S only because BODMAS is easier to say than BOMDAS. Children who read the letters literally get 24 ÷ 4 × 2 = 3 (wrong; it is 12) and 10 − 4 + 3 = 3 (wrong; it is 9). The single most useful sentence to say at home is: division and multiplication are the same step; addition and subtraction are the same step; go left to right.

BIDMAS (UK, Indices), PEMDAS (US, Parentheses and Exponents) and BEDMAS (Canada) are the same rule with different letters. PEMDAS puts M before D and gets the same wrong answers from children who read it literally in the other direction.

Why there is a rule at all

Without it, 2 + 3 × 4 is either 20 or 14 depending on who reads it. Mathematicians agreed that multiplication binds tighter than addition, so 2 + 3 × 4 means 2 + (3 × 4) = 14, and if you want 20 you write (2 + 3) × 4. Brackets exist to override the rule. That is all BODMAS is: the default reading, plus brackets to change it.

30 questions with answers

Time: Level 1 in 10 minutes, Level 2 in 12, Level 3 in 15. No calculator. Write one step per line.

Level 1 (Class 5, Year 6): brackets and the four operations

1. 8 + 2 × 5
2. (8 + 2) × 5
3. 20 − 12 ÷ 4
4. 36 ÷ (3 + 3)
5. 7 × 3 − 4 × 2
6. 15 − 6 + 3
7. 24 ÷ 4 × 2
8. 5 × (10 − 4) ÷ 3
9. 100 − 5 × 8 + 6
10. (14 − 5) × (2 + 3)

Answers: 1) 18 2) 50 3) 17 4) 6 5) 13 6) 12 7) 12 8) 10 9) 66 10) 45

Worked, question 5: 7 × 3 − 4 × 2. No brackets, no powers. Multiplications first, left to right: 21 − 8. Then subtract: 13.

Worked, question 7: 24 ÷ 4 × 2. Division and multiplication, left to right: 6 × 2 = 12. (Not 24 ÷ 8.)

Worked, question 9: 100 − 5 × 8 + 6. Multiply first: 100 − 40 + 6. Then left to right: 60 + 6 = 66.

Level 2 (Class 6, Year 7): powers and nested brackets

11. 3² + 4 × 2
12. (3 + 4)² − 10
13. 50 − 2 × 3²
14. 2 × (15 − (4 + 3))
15. 81 ÷ 3² + 5
16. (2 + 3)² − (2² + 3²)
17. 6 ÷ 2 × (1 + 2)
18. 5 + 3 × (12 ÷ 4)² − 7
19. 100 − 3² × 4
20. [(20 − 8) ÷ 4 + 1] × 5

Answers: 11) 17 12) 39 13) 32 14) 16 15) 14 16) 12 17) 9 18) 25 19) 64 20) 20

Worked, question 13: 50 − 2 × 3². Powers first: 3² = 9, so 50 − 2 × 9. Multiply: 50 − 18. Subtract: 32. (Not (2 × 3)² = 36; the power belongs to the 3 only.)

Worked, question 16: (2 + 3)² − (2² + 3²). Left bracket: 5² = 25. Right bracket: 4 + 9 = 13. Then 25 − 13 = 12. Note that (2 + 3)² is not 2² + 3²; this question is set to prove it.

Worked, question 17: 6 ÷ 2 × (1 + 2). Bracket: 6 ÷ 2 × 3. Left to right: 3 × 3 = 9.

Worked, question 20: [(20 − 8) ÷ 4 + 1] × 5. Innermost: 20 − 8 = 12. Then inside the square bracket: 12 ÷ 4 = 3, then 3 + 1 = 4. Then 4 × 5 = 20.

Level 3 (Class 7, Year 8): negative numbers, fractions, decimals

21. −3 + 4 × (−2)
22. (−3)² − 3²
23. 12 − (−4) × 2 ÷ (−8)
24. ½ × (6 + 10) − 2³
25. 0.5 × 8 + 3 × 0.2
26. (−2)³ + 10 ÷ (−5)
27. 3 × [7 − (2 − 5)]
28. (1/3 + 1/6) × 12 − 4
29. 40 ÷ (−4) − (−3) × 2
30. {[(6 + 2) × 3] − 4²} ÷ 2

Answers: 21) −11 22) 0 23) 11 24) 0 25) 4.6 26) −10 27) 30 28) 2 29) −4 30) 4

Worked, question 22: (−3)² − 3². The bracket: (−3)² = (−3) × (−3) = 9. Without the bracket, 3² = 9 and the minus sign stays: 9 − 9 = 0. This is the question that separates children who understand the bracket from those who do not: −3² on its own means −(3²) = −9.

Worked, question 23: 12 − (−4) × 2 ÷ (−8). Multiply and divide left to right: (−4) × 2 = −8; −8 ÷ (−8) = 1. Then 12 − 1 = 11.

Worked, question 30: {[(6 + 2) × 3] − 4²} ÷ 2. Innermost: 6 + 2 = 8. Then 8 × 3 = 24. Then 4² = 16 and 24 − 16 = 8. Then 8 ÷ 2 = 4.

The five mistakes behind most wrong answers

1. Doing D before M because the letters say so. 24 ÷ 4 × 2 = 12, left to right. Say "same step" every time.
2. Doing A before S for the same reason. 15 − 6 + 3 = 12, left to right, not 15 − 9 = 6.
3. Squaring the wrong thing. 2 × 3² means 2 × 9 = 18, not 6² = 36. The power sticks to the number (or bracket) directly in front of it.
4. Removing brackets too early. 2 × (15 − (4 + 3)): the inner bracket first, always, and rewrite the whole line each step so nothing is lost.
5. Losing the sign on a negative number. (−3)² = 9 but −3² = −9. Write the bracket if the negative is being squared.

Where it sits in each curriculum

Download the 30 questions with answers (PDF)

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics and teaches CBSE Class 5 to 8, KS2 and KS3, and US Grade 5 to 7 every week: the order of operations taught as "why" before "which letter", one step per line, and a marked worksheet after each class. The CBSE Class 6 to 8 maths page lists the chapters; the free 30-minute first class is a real lesson on this week's homework. The next topic most of these children meet is fractions, decimals and percentages.

Questions parents ask

See how we teach this, 1-on-1 online →