19 — Multiplication ranks above addition. 3 × 5 = 15. 4 + 15 = 19. Left to right would give 7 × 5 = 35.

Work out 20 − 12 ÷ 4.

17 — Division ranks above subtraction. 12 ÷ 4 = 3. 20 − 3 = 17. Left to right would give 8 ÷ 4 = 2.

Work out 8 + 2 × (5 − 1).

16 — Brackets first: 5 − 1 = 4. 8 + 2 × 4. Multiplication next: 2 × 4 = 8. 8 + 8 = 16. Left to right would give 10 × 4 = 40.

Work out 6 × 2 + 8 ÷ 4.

14 — Both the multiplication and the division rank above the addition, so do them first. 6 × 2 = 12. 8 ÷ 4 = 2. 12 + 2 = 14. Left to right would give 12 + 8 = 20, then ÷ 4 = 5.

Work out 48 ÷ 6 × 2.

16 — Division and multiplication share a rank, so work left to right. 48 ÷ 6 = 8. 8 × 2 = 16. Doing the multiplication first because M comes before D in BIDMAS gives 48 ÷ 12 = 4, which is wrong.

Work out 5 + 2² × 3.

17 — Indices first: 2² = 4. 5 + 4 × 3. Multiplication next: 4 × 3 = 12. 5 + 12 = 17. Left to right would square 7 to get 49, then × 3 = 147.

Work out (9 − 5)² ÷ 2.

8 — Brackets first: 9 − 5 = 4. 4² ÷ 2. Index next: 4² = 16. 16 ÷ 2 = 8. Squaring the 9 and the 5 separately would give 81 − 25 = 56, then ÷ 2 = 28.

Work out 24 ÷ (8 − 2 × 3).

12 — Work inside the bracket first, and the ranks still apply inside it. 2 × 3 = 6, so the bracket is 8 − 6 = 2. 24 ÷ 2 = 12. Simplifying the bracket left to right gives 6 × 3 = 18, then 24 ÷ (−10), which is not the intended sum.

Work out 100 − 4 × (3 + 2)².

0 — Bracket first: 3 + 2 = 5. 100 − 4 × 5². Index next: 5² = 25. Multiplication next: 4 × 25 = 100. 100 − 100 = 0.

Work out 2 × [30 − (4 + 5) × 2].

24 — Innermost bracket first: 4 + 5 = 9. 2 × [30 − 9 × 2]. Inside the outer bracket, multiplication ranks above subtraction: 9 × 2 = 18. 30 − 18 = 12. 2 × 12 = 24.

Work out the fraction with 12 + 8 on top and 5 − 1 underneath.

5 — A fraction bar brackets the whole of the top and the whole of the bottom. Top: 12 + 8 = 20. Bottom: 5 − 1 = 4. 20 ÷ 4 = 5. Typed into a calculator as 12 + 8 ÷ 5 − 1 it gives 12.6, which is a different calculation.

Work out 20 − 5 + 3.

18 — Addition and subtraction share a rank, so work left to right. 20 − 5 = 15. 15 + 3 = 18. Doing the addition first because A comes before S in BIDMAS gives 20 − 8 = 12, which is wrong.

Mathématiques

BIDMAS Practice Questions Where Left to Right Gives the Wrong Answer

Twelve expressions chosen so working left to right fails, each solved one operation per line, including division before multiplication and a nested bracket.

La réponse en bref
BIDMAS sets the order of a calculation: brackets, then indices, then division and multiplication together working left to right, then addition and subtraction together working left to right. So 4 + 3 × 5 = 19, not 35, and 48 ÷ 6 × 2 = 16, not 4.

Les exercices

Exercice 1Base1 points
Work out 4 + 3 × 5.
Afficher la correctionMasquer la correction
19
1. Multiplication ranks above addition.
2. 3 × 5 = 15.
3. 4 + 15 = 19.
4. Left to right would give 7 × 5 = 35.
Exercice 2Base1 points
Work out 20 − 12 ÷ 4.
Afficher la correctionMasquer la correction
17
1. Division ranks above subtraction.
2. 12 ÷ 4 = 3.
3. 20 − 3 = 17.
4. Left to right would give 8 ÷ 4 = 2.
Exercice 3Base2 points
Work out 8 + 2 × (5 − 1).
Afficher la correctionMasquer la correction
16
1. Brackets first: 5 − 1 = 4.
2. 8 + 2 × 4.
3. Multiplication next: 2 × 4 = 8.
4. 8 + 8 = 16. Left to right would give 10 × 4 = 40.
Exercice 4Base2 points
Work out 6 × 2 + 8 ÷ 4.
Afficher la correctionMasquer la correction
14
1. Both the multiplication and the division rank above the addition, so do them first.
2. 6 × 2 = 12.
3. 8 ÷ 4 = 2.
4. 12 + 2 = 14. Left to right would give 12 + 8 = 20, then ÷ 4 = 5.
Exercice 5Standard2 points
Work out 48 ÷ 6 × 2.
Afficher la correctionMasquer la correction
16
1. Division and multiplication share a rank, so work left to right.
2. 48 ÷ 6 = 8.
3. 8 × 2 = 16.
4. Doing the multiplication first because M comes before D in BIDMAS gives 48 ÷ 12 = 4, which is wrong.
Exercice 6Standard2 points
Work out 5 + 2² × 3.
Afficher la correctionMasquer la correction
17
1. Indices first: 2² = 4.
2. 5 + 4 × 3.
3. Multiplication next: 4 × 3 = 12.
4. 5 + 12 = 17. Left to right would square 7 to get 49, then × 3 = 147.
Exercice 7Standard2 points
Work out (9 − 5)² ÷ 2.
Afficher la correctionMasquer la correction
8
1. Brackets first: 9 − 5 = 4.
2. 4² ÷ 2.
3. Index next: 4² = 16.
4. 16 ÷ 2 = 8. Squaring the 9 and the 5 separately would give 81 − 25 = 56, then ÷ 2 = 28.
Exercice 8Standard3 points
Work out 24 ÷ (8 − 2 × 3).
Afficher la correctionMasquer la correction
12
1. Work inside the bracket first, and the ranks still apply inside it.
2. 2 × 3 = 6, so the bracket is 8 − 6 = 2.
3. 24 ÷ 2 = 12.
4. Simplifying the bracket left to right gives 6 × 3 = 18, then 24 ÷ (−10), which is not the intended sum.
Exercice 9Approfondi3 points
Work out 100 − 4 × (3 + 2)².
Afficher la correctionMasquer la correction
0
1. Bracket first: 3 + 2 = 5.
2. 100 − 4 × 5².
3. Index next: 5² = 25.
4. Multiplication next: 4 × 25 = 100.
5. 100 − 100 = 0.
Exercice 10Approfondi4 points
Work out 2 × [30 − (4 + 5) × 2].
Afficher la correctionMasquer la correction
24
1. Innermost bracket first: 4 + 5 = 9.
2. 2 × [30 − 9 × 2].
3. Inside the outer bracket, multiplication ranks above subtraction: 9 × 2 = 18.
4. 30 − 18 = 12.
5. 2 × 12 = 24.
Exercice 11Approfondi3 points
Work out the fraction with 12 + 8 on top and 5 − 1 underneath.
Afficher la correctionMasquer la correction
5
1. A fraction bar brackets the whole of the top and the whole of the bottom.
2. Top: 12 + 8 = 20.
3. Bottom: 5 − 1 = 4.
4. 20 ÷ 4 = 5.
5. Typed into a calculator as 12 + 8 ÷ 5 − 1 it gives 12.6, which is a different calculation.
Exercice 12Approfondi2 points
Work out 20 − 5 + 3.
Afficher la correctionMasquer la correction
18
1. Addition and subtraction share a rank, so work left to right.
2. 20 − 5 = 15.
3. 15 + 3 = 18.
4. Doing the addition first because A comes before S in BIDMAS gives 20 − 8 = 12, which is wrong.

Où l'on se trompe

Working straight through from left to right, so 4 + 3 × 5 comes out as 35.
Treating BIDMAS as six ranks rather than four, so 48 ÷ 6 × 2 is answered as 4 and 20 − 5 + 3 as 12.
Applying an index to the wrong quantity, squaring 5 + 2 in 5 + 2² × 3, or squaring 9 and 5 separately in (9 − 5)².
Simplifying the contents of a bracket left to right, so 8 − 2 × 3 becomes 18 instead of 2.
Ignoring the fraction bar as a grouping symbol when transferring an expression to a calculator.

What BIDMAS gets wrong about itself

Read as six ranked steps, BIDMAS produces wrong answers. Division and multiplication share one rank and are done left to right; addition and subtraction share the rank below and are also done left to right. The acronym has to name them in some order, and the order it picks is not a priority.

This is why 48 ÷ 6 × 2 is 16 and not 4. Division comes first here because it comes first on the page, not because division outranks multiplication. The same trap sits under 20 − 5 + 3, which is 18: doing the addition first because A comes before S in the acronym gives 12.

Eleven of the twelve questions below punish reading left to right and ignoring the ranks. The last one punishes the opposite — taking BIDMAS too literally as six steps.

One operation per line

Every answer below is written with one operation carried out per line and everything else copied down unchanged. It looks slow and it is the fastest way to stop losing marks, because it makes each step separately checkable and it removes the temptation to do two things at once in your head.

It also fixes the most common cause of a lost mark in these questions, which is not the order at all — it is copying a number wrongly while rushing to the answer. If 100 − 4 × (3 + 2)² is written out as 100 − 4 × 5², then 100 − 4 × 25, then 100 − 100, then 0, there is nowhere for a digit to go missing.

Brackets that are not written as brackets

A fraction bar groups everything above it and everything below it, as if each had brackets round it. Typing (12 + 8) ÷ (5 − 1) into a calculator as 12 + 8 ÷ 5 − 1 is a different sum entirely, and the calculator will answer the one you typed.

A square root sign does the same job, and so does the bracket inside a bracket: in 2 × [30 − (4 + 5) × 2] the inner bracket is resolved first, then the multiplication inside the outer one, then the subtraction, and only then the multiplication by 2.

In England, the order of operations is introduced in Year 6, where pupils are expected to use it in calculations involving all four operations.

Questions fréquentes

Is it BIDMAS, BODMAS or PEMDAS?

They are the same rule with different local wording. The B or P is brackets or parentheses; the I or O or E is indices, "of", or exponents. PEMDAS is the American version and appears in SAT material. Whichever spelling is used, DM is one rank read left to right and AS is the rank below, also read left to right.

Why is 48 ÷ 6 × 2 equal to 16 and not 4?

Because division and multiplication have equal priority and are carried out in the order they appear. 48 ÷ 6 = 8 comes first because it is written first, then 8 × 2 = 16. The M sitting before the D in the acronym is only spelling; it does not promote multiplication above division.

Do calculators follow BIDMAS?

Modern scientific calculators do, and simple four-function calculators often do not — they apply each operation as you press it. That difference is worth testing on your own machine with 4 + 3 × 5: an answer of 19 means it follows the ranks, and 35 means it does not and every calculation needs bracketing by hand.

When do pupils in England learn the order of operations?

It is introduced in Year 6, where pupils use their knowledge of the order of operations in calculations involving all four operations. It then reappears constantly through secondary school, since substituting into a formula, expanding brackets and evaluating an expression all depend on it being automatic.

Sources

National curriculum in England: mathematics programmes of study — Department for Education

Dernière mise à jour 21 août 2026