What does BIDMAS stand for in Mathematics?

BIDMAS is an acronym used in Mathematics to remember the order of operations. It stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction. This order is crucial for solving mathematical expressions correctly, especially in the IB MYP curriculum.

Why is the order of operations important in Mathematics?

The order of operations, often remembered by the acronym BIDMAS, is important because it ensures that mathematical expressions are solved consistently and correctly. Without a standard order, different people might interpret and solve the same expression in different ways, leading to varied results. This is particularly emphasized in the IB MYP Mathematics curriculum to develop a strong foundational understanding.

How do you apply BIDMAS in solving mathematical expressions?

To apply BIDMAS, start by solving any operations inside Brackets, then move on to Indices (exponents). Next, perform Division and Multiplication from left to right, followed by Addition and Subtraction, also from left to right. This systematic approach helps in accurately solving complex expressions, a skill emphasized in the IB MYP Mathematics program.

Can you provide an example of using BIDMAS in a mathematical expression?

Certainly! Consider the expression 3 + 6 × (5 + 4) ÷ 3 - 7. According to BIDMAS, solve the Brackets first: 5 + 4 = 9. Then, the expression becomes 3 + 6 × 9 ÷ 3 - 7. Next, perform the Multiplication and Division from left to right: 6 × 9 = 54, and 54 ÷ 3 = 18. The expression now is 3 + 18 - 7. Finally, perform Addition and Subtraction from left to right: 3 + 18 = 21, and 21 - 7 = 14. Thus, the answer is 14.

What common mistakes should students avoid when using BIDMAS?

A common mistake is not following the correct order, such as performing Addition before Division. Another error is misunderstanding that Division and Multiplication, as well as Addition and Subtraction, are performed from left to right, not strictly in the order of BIDMAS. Students should also be careful with negative numbers and ensure they correctly interpret brackets. These pitfalls are often addressed in the IB MYP Mathematics curriculum to enhance problem-solving skills.

Why is "Doing all multiplication before any division." a common mistake in BIDMAS?

Why it happens: Misreading 'BIDMAS' as a strict left-to-right hierarchy. How to avoid it: × and ÷ share priority — work LEFT to RIGHT when they appear together.

Why is "Writing $-3^2 = 9$." a common mistake in BIDMAS?

Why it happens: Treating the negative sign as part of the base. How to avoid it: -3^2 means -(3^2) = -9. Only (-3)^2 = 9. Always bracket a negative being squared.

Why is "Substituting without brackets: $x = -4$, $x^2 = -4^2 = -16$." a common mistake in BIDMAS?

Why it happens: Skipped bracketing. How to avoid it: Always write x = (-4), then x^2 = (-4)^2 = 16. Brackets are essential when substituting negatives.

NumberIB MYP Maths Extended Level

BIDMAS

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BIDMAS — IB MYP Mathematics (Extended): the order of operations

Mathematics is ambiguous without a convention for the order of operations. This MYP Mathematics Extended note covers BIDMAS, when to use brackets, and how to avoid the most common trap.

What you’ll learn

Mapped to the IB MYP Mathematics subject guide (2026 onwards).

MYP Mathematics A — Apply BIDMAS to evaluate complex expressions.
MYP Mathematics C — Use brackets to remove ambiguity in your written work.
MYP Mathematics D — Translate real situations into expressions with correct order.

The order

Five priority levels — but $\times\div$ and $+-$ each share a level.

BIDMAS gives a strict order in which to apply operations:

Priority	Operation
1	Brackets — innermost first
2	Indices (powers, roots)
3	Division and Multiplication — equal priority, left to right
4	Addition and Subtraction — equal priority, left to right

The crucial subtlety is rows 3 and 4: $\times$ and $\div$ share priority — you don't always do multiplication before division. You do them LEFT to RIGHT in the order they appear.

BIDMAS pyramid. Rows 3 and 4 share priority within themselves — work left-to-right when they tie.

Common ambiguity. $20 \div 4 \times 5$ . Multiplication first? NO — equal priority, work left to right. $20 \div 4 \times 5 = 5 \times 5 = 25.$ (Not $20 \div 20 = 1$ .)

B–I–DM–AS (DM share priority, AS share priority).
Equal priority $\to$ left to right.
Inner brackets first when nested.

Worked examples

Apply BIDMAS step by step.

Example 1. Evaluate $5 + 2 \times 3$ .

Multiplication first: $2 \times 3 = 6$ .
Then addition: $5 + 6 = 11$ .

Example 2. Evaluate $(5 + 2) \times 3$ .

Brackets first: $5 + 2 = 7$ .
Then multiplication: $7 \times 3 = 21$ .

Example 3. Evaluate $3 + 4^2 - (10 - 6) \div 2$ .

Brackets: $(10-6) = 4$ . Expression: $3 + 4^2 - 4 \div 2$ .
Indices: $4^2 = 16$ . Expression: $3 + 16 - 4 \div 2$ .
Division: $4 \div 2 = 2$ . Expression: $3 + 16 - 2$ .
Add/subtract left to right: $3 + 16 = 19$ ; $19 - 2 = 17$ .

Example 4 (Extended-level). Evaluate $\dfrac{4 + 6}{5} - 3^2 + \sqrt{16}$ .

The horizontal fraction bar acts like a bracket. Top: $4 + 6 = 10$ . Expression: $\dfrac{10}{5} - 3^2 + \sqrt{16}$ .
Indices and root: $3^2 = 9$ and $\sqrt{16} = 4$ . Expression: $2 - 9 + 4$ .
Add/subtract left to right: $2 - 9 = -7$ ; $-7 + 4 = -3$ .

Example 5. Evaluate $-2^2$ versus $(-2)^2$ .

$-2^2 = -(2^2) = -4$ (indices apply to 2, then the minus sign).
$(-2)^2 = (-2) \times (-2) = 4$ .

These are NOT the same — use brackets to be clear about what is being squared.

Always rewrite the whole expression after each step.
The fraction bar (and $\sqrt{\ }$ ) acts like a bracket.
Negatives are NOT squared unless inside brackets.

When to add extra brackets

Brackets are free — use them.

Examiners love to see clear notation. Use brackets even when the rule technically lets you omit them. Three good times to add brackets:

Around any negative number you'll square or take a power of: $(-3)^2$ , not $-3^2$ .
Around a sum or difference inside a product: $5 \times (2 + 3)$ is clearer than relying on order.
In substitution. If $x = -4$ , then $x^2 = (-4)^2 = 16$ . Forgetting brackets here will lose you marks.

For Extended-level algebra and calculus, getting BIDMAS wrong in substitution is one of the most common mark-losers. Always use brackets around the value you substitute.

For criterion C (Communicating), your working is graded as much for CLARITY as correctness. Brackets cost nothing and prevent ambiguity.

Add brackets around any number you'll then raise to a power.
Add brackets when substituting values — especially negatives.
Use brackets to make your working unambiguous (criterion C).

How it’s examined

Criterion A: rapid evaluation of expressions. Criterion C: well-structured working with brackets. Criterion D: model word problems into expressions with correct order.

Sources: IB MYP Mathematics subject guide (IBO, official). Last reviewed 2026-05-25.

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Step-by-step worked examples — BIDMAS

Step-by-step solutions to past-paper-style questions on bidmas, written exactly the way a tutor would explain them at the board.

1Basic BIDMAS
Getting started• order
Question
Evaluate $7 + 6 \times 2 - 3$ .
Step-by-step solution
1. Step 1
  Multiplication first: $6 \times 2 = 12$ . Expression: $7 + 12 - 3$ .
2. Step 2
  Add/subtract left to right: $7 + 12 = 19$ ; $19 - 3 = 16$ .
Answer
$16$
2Equal-priority trap
Building confidence• division
Question
Evaluate $24 \div 6 \times 2$ .
Step-by-step solution
1. Step 1
  $\div$ and $\times$ share priority — work LEFT to RIGHT.
2. Step 2
  $24 \div 6 = 4$ . Expression: $4 \times 2$ .
3. Step 3
  $4 \times 2 = 8$ .
Answer
$8$ (NOT $24 \div 12 = 2$ ).
3Indices with a negative
Building confidence• indices
Question
Evaluate (a) $-5^2$ and (b) $(-5)^2$ .
Step-by-step solution
1. Step 1
  (a) $-5^2$ : indices apply to the 5 only. $5^2 = 25$ . Then the minus sign: $-25$ .
2. Step 2
  (b) $(-5)^2$ : brackets first. The whole $-5$ is squared: $(-5) \times (-5) = 25$ .
Answer
(a) $-25$ (b) $25$
4Nested brackets
Stretch• brackets
Question
Evaluate $20 - 3 \times \left[ 2 + (5 - 1)^2 \right]$ .
Step-by-step solution
1. Step 1
  Innermost brackets: $(5-1) = 4$ . Expression: $20 - 3 \times [ 2 + 4^2 ]$ .
2. Step 2
  Indices inside the outer bracket: $4^2 = 16$ . Expression: $20 - 3 \times [2 + 16]$ .
3. Step 3
  Sum inside outer bracket: $2 + 16 = 18$ . Expression: $20 - 3 \times 18$ .
4. Step 4
  Multiplication before subtraction: $3 \times 18 = 54$ . Expression: $20 - 54 = -34$ .
Answer
$-34$

Key Definitions and Keywords — BIDMAS

Definitions to memorise and the exact keywords mark schemes credit for bidmas answers — sharpened from recent examiner reports for the 2026 IB MYP Mathematics (Extended) sitting.

BIDMAS
Examiner keyword
Mnemonic for the order of operations: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
Indices (powers/exponents)
Examiner keyword
The notation $a^n$ means $a$ multiplied by itself $n$ times.
Implicit brackets
The fraction bar and square-root symbol act like brackets — evaluate inside them first.

Common Mistakes and Misconceptions — BIDMAS

The traps other students keep falling into on bidmas questions — taken from recent IB MYP Mathematics (Extended) examiner reports and mark schemes — and how to avoid them.

✕Doing all multiplication before any division.
Why it happens
Misreading 'BIDMAS' as a strict left-to-right hierarchy.
How to avoid it
$\times$ and $\div$ share priority — work LEFT to RIGHT when they appear together.
✕Writing $-3^2 = 9$ .
Why it happens
Treating the negative sign as part of the base.
How to avoid it
$-3^2$ means $-(3^2) = -9$ . Only $(-3)^2 = 9$ . Always bracket a negative being squared.
✕Substituting without brackets: $x = -4$ , $x^2 = -4^2 = -16$ .
Why it happens
Skipped bracketing.
How to avoid it
Always write $x = (-4)$ , then $x^2 = (-4)^2 = 16$ . Brackets are essential when substituting negatives.

Practice questions

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BIDMAS — frequently asked questions

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BIDMAS

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Detailed Notes

What you’ll learn

How it’s examined

1Basic BIDMAS

2Equal-priority trap

3Indices with a negative

4Nested brackets

BIDMAS

Indices (powers/exponents)

Implicit brackets

✕Doing all multiplication before any division.

✕Writing −32=9-3^2 = 9−32=9.

✕Substituting without brackets: x=−4x = -4x=−4, x2=−42=−16x^2 = -4^2 = -16x2=−42=−16.

Practice questions

Past paper style quiz

Assess your understanding

BIDMAS — frequently asked questions

✕Writing $-3^2 = 9$ .

✕Substituting without brackets: $x = -4$ , $x^2 = -4^2 = -16$ .