BODMAS Rules Made Simple : Solve Any Math Calculation Right

  BODMAS Rules Made Simple: The RightOrder for Solving Any Calculation You’re working through a quick calculation—perhaps splitting a bill...

 

BODMAS Rules Made Simple: The RightOrder for Solving Any Calculation

You’re working through a quick calculation—perhaps splitting a bill, checking a discount, or helping with homework—and get an answer that doesn’t match the calculator. The numbers look straightforward. So where did things go wrong?

Often, the culprit is the order of operations. BODMAS is a memory aid that tells you which parts of a mathematical expression to calculate first. Learn how it works, and calculations that once seemed ambiguous become much easier to tackle.

This guide explains the rules of BODMAS, clears up common misunderstandings, and walks through examples from simple sums to tricky expressions. You’ll also learn why multiplication and division share priority, how brackets affect a calculation, and how to check your answer confidently.

What Does BODMAS Mean?

BODMAS is an acronym for the order in which mathematical operations are performed:

Letter	Meaning	Examples
B	Brackets	( ), [ ], { }
O	Orders, or powers and roots	3², √16, 2³
D	Division	÷, /
M	Multiplication	×, ·
A	Addition	+
S	Subtraction	−

BODMAS helps everyone read and solve mathematical expressions consistently. Without an agreed order, an expression such as $8 + 2 \times 5$ could be interpreted in more than one way. BODMAS removes that uncertainty.

The basic idea

Work through the expression in this order:

• 1.       Calculate anything inside brackets.
• 2.       Evaluate powers and roots.
• 3.       Perform division and multiplication, moving from left to right.
• 4.       Perform addition and subtraction, moving from left to right.

The key detail is that division does not always come before multiplication, even though D appears before M in the acronym. They have equal priority. Likewise, addition and subtraction have equal priority.

That means BODMAS is best understood as four levels:

• 1.       Brackets
• 2.       Orders
• 3.       Multiplication and division, from left to right
• 4.       Addition and subtraction, from left to right

A quick example

Consider:

6 + 3 × 4

Multiplication has priority over addition, so calculate 3 × 4 first:

6 + 12 = 18

The answer is 18, not 36. Calculating from left to right without considering the order of operations would give (6 + 3) × 4 = 36, but there are no brackets telling us to add first.

A useful principle: BODMAS is not a suggestion to work through every letter separately. It is a way to group operations by priority.

BODMAS and other versions

You may also see the same idea written as BIDMAS, BEDMAS, or PEMDAS. These names vary by country and curriculum:

1. ·         BIDMAS: Brackets, Indices, Division, Multiplication, Addition, Subtraction
2. ·         BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction
3. ·         PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

The wording differs, but the core convention is the same: brackets first, powers and roots next, then multiplication/division and addition/subtraction at equal priority within their respective pairs.

How to Apply BODMAS Step by Step

The easiest way to use BODMAS is to treat it like a checklist. Don’t try to do everything in your head at once. Identify the highest-priority operation, calculate it, and rewrite the expression.

Step 1: Work inside brackets

Brackets show that a group of operations belongs together. Calculate the contents of the innermost brackets first, then work outward.

Example:

5 × (2 + 6)

First solve the bracket:

2 + 6 = 8

Then multiply:

5 × 8 = 40

So the answer is 40.

Compare that with:

5 × 2 + 6

There are no brackets, so multiplication comes first:

10 + 6 = 16

The brackets change the meaning of the expression. They are not decorative.

Step 2: Calculate powers and roots

After brackets, evaluate orders: powers, indices, exponents, and roots.

Example:

4 + 3²

Calculate the square first:

3² = 9

Then add:

4 + 9 = 13

A common mistake is to read 3² as 3 × 2. It means 3 × 3, which equals 9.

Another example:

20 − √16 × 2

First evaluate the square root:

√16 = 4

Then multiply:

4 × 2 = 8

Finally subtract:

20 − 8 = 12

Step 3: Do multiplication and division from left to right

Multiplication and division have equal priority. When both appear, work from left to right.

Example:

24 ÷ 6 × 2

Move left to right:

24 ÷ 6 = 4

Then:

4 × 2 = 8

The answer is 8.

It is incorrect to automatically do the multiplication first just because multiplication appears in the acronym after division. The letters help you remember which operations share a level; they do not override the left-to-right rule.

Another example:

36 ÷ 3 × 4 ÷ 2

Work left to right:

·         36 ÷ 3 = 12

·         12 × 4 = 48

·         48 ÷ 2 = 24

The answer is 24.

Step 4: Do addition and subtraction from left to right

Addition and subtraction also share priority.

Example:

15 − 4 + 2

Work from left to right:

15 − 4 = 11

Then:

11 + 2 = 13

The answer is 13.

Do not assume addition must always come before subtraction. The same left-to-right rule applies.

A complete worked example

Solve:

8 + 2 × (9 − 5)² ÷ 4

Follow the checklist:

1.       Brackets: 9 − 5 = 4Expression becomes 8 + 2 × 4² ÷ 4

2.       Orders: 4² = 16Expression becomes 8 + 2 × 16 ÷ 4

3.       Multiplication and division, left to right:2 × 16 = 32, then 32 ÷ 4 = 8

4.       Addition: 8 + 8 = 16

The answer is 16.

Writing each new line makes it easier to spot mistakes. It also shows exactly how the original expression changes at each stage.

Tricky BODMAS Rules That Cause Confusion

Most errors don’t happen because someone has never heard of BODMAS. They happen because the shorthand is misunderstood. Here are the points worth getting straight.

Multiplication and division are equal in priority

This is the most common BODMAS confusion. The acronym lists D before M, but division does not automatically outrank multiplication.

For example:

18 ÷ 3 × 2

Correct approach: move left to right.

18 ÷ 3 = 66 × 2 = 12

Answer: 12

If you multiply 3 × 2 first, you get 18 ÷ 6 = 3, which changes the expression’s meaning. There are no brackets telling you to group 3 × 2.

Addition and subtraction are equal in priority

The same principle applies to addition and subtraction.

20 − 8 + 3

Move left to right:

20 − 8 = 1212 + 3 = 15

Answer: 15

You could rewrite subtraction as adding a negative:

20 + (−8) + 3

That makes the left-to-right result easier to see.

A fraction bar acts like grouping

A horizontal fraction bar groups the entire numerator and denominator. It works much like brackets.

For example:

\(\frac{6+2}{4}\)

The numerator is 6 + 2, so calculate it as a group:

8 ÷ 4 = 2

But:

6 + 2 ÷ 4

has no grouping around 6 + 2. Division comes first:

6 + 0.5 = 6.5

A fraction bar can therefore change which operations are grouped together. When typing a fraction into a calculator, use parentheses if needed: (6 + 2) / 4.

Brackets can be nested

When brackets appear inside other brackets, solve from the inside out.

Example:

3 × [2 + (8 − 5)]

First solve the innermost bracket:

8 − 5 = 3

Then the square bracket:

2 + 3 = 5

Finally multiply:

3 × 5 = 15

Different bracket styles—parentheses ( ), square brackets [ ], and braces { }—often help make nested expressions easier to read. They do not usually represent different operations.

Negative numbers need careful handling

A minus sign can mean subtraction, or it can be part of a negative number. Brackets help make the distinction clear.

For example:

−3²

By standard convention, the exponent is evaluated before the leading negative sign:

−3² = −(3²) = −9

But:

(−3)² = (−3) × (−3) = 9

Those expressions are different. If you mean to square the negative number, include it in brackets.

Powers of powers

When raising a power to another power, apply the exponent rules carefully:

(2³)²

First calculate inside the brackets:

2³ = 8

Then square the result:

8² = 64

You can also use the exponent rule (aᵐ)ⁿ = aᵐⁿ:

(2³)² = 2⁶ = 64

But don’t confuse this with 2³², which is a different expression.

Implied multiplication can look ambiguous

Expressions such as 6 ÷ 2(1 + 2) can cause disagreement because different calculators and conventions may interpret the implied multiplication differently. The safest approach is to add explicit brackets or a fraction bar.

If the intended calculation is:

6 ÷ [2 × (1 + 2)]

then:

6 ÷ [2 × 3] = 6 ÷ 6 = 1

If the intended calculation is:

(6 ÷ 2) × (1 + 2)

then:

3 × 3 = 9

When an expression is ambiguous, don’t rely on a slogan or a calculator display. Rewrite it clearly.

Common BODMAS Mistakes—and How to Avoid Them

Knowing the rule is one thing; applying it consistently is another. These habits help prevent the most frequent errors.

Mistake 1: Solving strictly from left to right

Left-to-right working applies within operations of equal priority, not to the entire expression.

Incorrect approach:

7 + 2 × 59 × 5 = 45

Correct approach:

2 × 5 = 107 + 10 = 17

Fix: Identify the operation with the highest priority before calculating.

Mistake 2: Treating D and M as separate ranks

The letters make it tempting to divide first wherever division appears, then multiply. That is not the rule.

For:

48 ÷ 6 × 3

Work from left to right:

48 ÷ 6 = 88 × 3 = 24

Fix: Think “multiplication and division together, left to right.”

Mistake 3: Treating A and S as separate ranks

For:

30 − 12 + 5

Work left to right:

30 − 12 = 1818 + 5 = 23

Fix: Think “addition and subtraction together, left to right.”

Mistake 4: Forgetting what a fraction bar groups

A fraction bar applies to everything written in the numerator and denominator, unless the layout says otherwise.

Fix: Rewrite the fraction using parentheses before entering it into a calculator. For example, write (a + b) / (c − d) rather than typing a string of symbols that could be misread.

Mistake 5: Misreading a negative exponent or sign

−4² and (−4)² are not the same.

Fix: Add brackets around negative numbers when they are part of a power or another operation.

Mistake 6: Skipping steps

Mental arithmetic can be efficient, but it makes it harder to catch where an error occurred.

Fix: Rewrite the expression after each major operation, especially in longer problems. One line per step is usually enough.

Mistake 7: Assuming a calculator will interpret everything as intended

Calculators differ in how they handle implied multiplication, input formats, and parentheses. A calculator can evaluate what you typed, but it cannot always know what you meant.

Fix: Use explicit multiplication symbols and brackets. If two people get different answers, compare how they entered the expression.

A quick self-check routine

Before settling on an answer, ask:

1.  Did I calculate brackets first?
2. Did I evaluate powers and roots?
3. Did I handle multiplication and division from left to right?
4. Did I handle addition and subtraction from left to right?
5. Did I copy the expression correctly?
6. Are any negative numbers or fraction bars ambiguous?

 If the answer passes those checks, you’re much less likely to have made a BODMAS error.

Practice Problems: Put the BODMAS Rules to Work

The best way to make the order of operations feel natural is to practise. Try each problem before looking at the working.

Problem 1: A simple priority check

9 + 4 × 3

Multiplication first:

4 × 3 = 12

Then addition:

9 + 12 = 21

Answer: 21

Problem 2: Brackets change the result

(9 + 4) × 3

Brackets first:

9 + 4 = 13

Then multiply:

13 × 3 = 39

Answer: 39

Notice how adding brackets changed the answer from 21 to 39.

Problem 3: Powers and division

5 + 2³ ÷ 4

First calculate the power:

2³ = 8

Then divide:

8 ÷ 4 = 2

Then add:

5 + 2 = 7

Answer: 7

Problem 4: Multiplication and division at the same level

42 ÷ 7 × 3

Work left to right:

42 ÷ 7 = 66 × 3 = 18

Answer: 18

Problem 5: Addition and subtraction at the same level

14 + 6 − 9

Work left to right:

14 + 6 = 2020 − 9 = 11

Answer: 11

Problem 6: Nested brackets

2 × {5 + [12 ÷ (6 − 2)]}

Start inside:

6 − 2 = 4

Then divide:

12 ÷ 4 = 3

Then add:

5 + 3 = 8

Finally multiply:

2 × 8 = 16

Answer: 16

Problem 7: Negative numbers and powers

(−5)² − 3 × 4

First square the number in brackets:

(−5)² = 25

Then multiply:

3 × 4 = 12

Then subtract:

25 − 12 = 13

Answer: 13

Problem 8: A longer mixed expression

18 − 2 × (3 + 1)² ÷ 4

Brackets:

3 + 1 = 4

Orders:

4² = 16

Multiplication and division from left to right:

2 × 16 = 3232 ÷ 4 = 8

Subtraction:

18 − 8 = 10

Answer: 10

A practical way to build confidence

When practicing, don’t focus only on getting the final number. Explain why each operation comes next. For example:

“I’m doing the brackets first. Then I’ll evaluate the power. Multiplication and division are next, from left to right. Addition comes last.”

That short explanation turns BODMAS from a memorized acronym into a method you can apply to unfamiliar problems.

Common Doubts Clarified

1. What does BODMAS stand for?

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. It is a memory aid for the order of operations.

2. What is the correct order of operations in BODMAS?

Calculate brackets first, then powers and roots. Next, do multiplication and division from left to right. Finally, do addition and subtraction from left to right.

3. Is BODMAS a rule or just a memory trick?

It is a memory aid for standard mathematical conventions. The important rules are the priority of operations and the left-to-right approach for operations with equal priority.

4. Do you always do division before multiplication?

No. Division and multiplication have equal priority. Work through them from left to right.

5. Do you always do addition before subtraction?

No. Addition and subtraction have equal priority. Work through them from left to right.

6. What is the answer to 8 + 2 × 5?

Multiply first: 2 × 5 = 10. Then add: 8 + 10 = 18.

7. What is the answer to 24 ÷ 6 × 2?

Work left to right: 24 ÷ 6 = 4, then 4 × 2 = 8.

8. Why do multiplication and division have equal priority?

They are inverse operations at the same level in the standard order of operations. The left-to-right convention ensures that an expression has one consistent interpretation.

9. Why do addition and subtraction have equal priority?

Addition and subtraction are inverse operations at the same level. When both appear, calculate them in the order they occur from left to right.

10. What does “Orders” mean in BODMAS?

“Orders” generally means powers, indices, exponents, and roots. For example, 5² and √25 are orders.

11. Are brackets always calculated first?

Yes. Start with the innermost brackets, then work outward. If an expression has no brackets, move to the next priority level.

12. Does a fraction bar act like brackets?

Yes. A fraction bar groups the numerator and denominator. For example, (a + b) / c means add a and b before dividing by c.

13. What is the difference between BODMAS and BIDMAS?

They describe the same order of operations. In BIDMAS, the “I” stands for indices, while “O” in BODMAS stands for orders.

14. What is the difference between BODMAS and PEMDAS?

They are regional variations of the same convention. PEMDAS uses “Parentheses” and “Exponents,” while BODMAS uses “Brackets” and “Orders.” Both require multiplication/division and addition/subtraction to be handled left to right.

15. Is multiplication always done before addition?

Yes. Multiplication has higher priority than addition unless brackets change the grouping.

16. What is the answer to 10 − 3 + 2?

Work left to right: 10 − 3 = 7, then 7 + 2 = 9.

17. What is the answer to 3 + 4²?

Evaluate the power first: 4² = 16. Then add: 3 + 16 = 19.

18. Is −3² equal to 9?

Under standard conventions, −3² means −(3²), which equals −9. By contrast, (−3)² equals 9.

19. How do I solve an expression with nested brackets?

Start with the innermost bracket, calculate it, and then work outward. Once all brackets are resolved, continue with powers, multiplication/division, and addition/subtraction.

20. Can I solve BODMAS problems from left to right?

Only for operations at the same priority level. For example, multiplication and division are handled left to right, but addition does not come before multiplication.

21. Why do people get different answers to the same expression?

They may be applying the order differently, interpreting an ambiguous expression differently, or entering it into a calculator with different brackets. Rewrite unclear expressions with explicit parentheses.

22. How should I enter BODMAS calculations into a calculator?

Use brackets to show grouping and include explicit multiplication symbols. For example, enter (6 + 2) / 4 rather than relying on a fraction layout or implied multiplication.

23. What should I do with implied multiplication, such as 2(3 + 4)?

Treat it as multiplication: 2 × (3 + 4). If the expression also includes division and its meaning is unclear, add brackets to show the intended grouping.

24. Is 6 ÷ 2(1 + 2) ambiguous?

It can be interpreted differently depending on notation and calculator conventions. Write the intended grouping explicitly, such as 6 ÷ [2 × (1 + 2)] or (6 ÷ 2) × (1 + 2).

25. Are square brackets and curly braces different from parentheses?

They usually serve the same purpose: grouping. Different shapes are often used to make nested expressions easier to read.

26. What is the best way to avoid BODMAS mistakes?

Work one step at a time, rewrite the expression after each operation, and remember that multiplication/division and addition/subtraction are handled left to right.

27. Does BODMAS apply to algebra?

Yes. The same order of operations applies when expressions contain variables. For example, in 3 + 2x, multiplication is understood before addition, so the expression means 3 + (2 × x).

28. Does BODMAS apply to calculators and computers?

The underlying conventions apply, but input systems can handle certain shorthand expressions differently. Use explicit brackets and check how the device interprets the expression.

29. Can brackets be used just to make an expression clearer?

Yes. Brackets can make grouping explicit, even when they are not strictly necessary. Clear notation is especially helpful in longer calculations.

30. What is the simplest way to remember BODMAS?

Remember the four levels: brackets; powers and roots; multiplication and division left to right; addition and subtraction left to right.

Make the Order Clear, Then Work It Through

BODMAS is less about memorizing six letters and more about following a reliable sequence. Handle brackets first, evaluate powers and roots, then move through multiplication and division from left to right, followed by addition and subtraction from left to right.

When an expression looks confusing, slow it down. Add brackets where the grouping is unclear, show one step per line, and check that you haven’t given one operation an unfair priority. With that habit, even a long calculation becomes a series of manageable decisions.

Try the practice problems above, then write one of your own and solve it step by step. That’s the quickest way to make the rules stick.

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