What Is BIDMAS/BODMAS?

BIDMAS and BODMAS are acronyms that help students remember the standard order of operations. The order of operations is the rule mathematicians use to decide which part of a calculation should be completed first when an expression contains more than one operation. Without this rule, a short expression such as 3 + 4 x 5 could give different answers depending on who reads it. One person might add first and get 35. Another person might multiply first and get 23. The agreed mathematical answer is 23 because multiplication is done before addition.

The names are different in different countries and classrooms. Many UK classrooms use BIDMAS. Many UK and Indian classrooms use BODMAS. Many US classrooms use PEMDAS. These acronyms look different, but they describe the same convention. Brackets, parentheses and grouping symbols are first. Indices, orders and exponents are next. Division and multiplication share one level. Addition and subtraction share the last level.

The most important sentence in this whole guide is this: division does not always come before multiplication, and addition does not always come before subtraction. In the acronym, D appears before M and A appears before S, but that does not mean D must always happen before M or A must always happen before S. Division and multiplication have equal priority, so you work left to right. Addition and subtraction also have equal priority, so you work left to right.

This left-to-right point is where many BIDMAS mistakes happen. For example, 24 / 3 x 2 is not 24 / (3 x 2). You read division and multiplication from left to right: 24 / 3 = 8, then 8 x 2 = 16. The correct answer is 16, not 4. If the writer wanted 4, they should have written 24 / (3 x 2).

BIDMAS, BODMAS and PEMDAS Compared

Students often worry that BIDMAS, BODMAS and PEMDAS are different rules. They are not. They are different labels for the same priority system. The words change because different countries and teachers prefer different vocabulary. Indices, orders and exponents all describe powers such as 2^3, square roots such as sqrt(49), and other repeated-power operations.

The acronym is useful, but the underlying idea is more important than memorizing letters. Mathematicians use operations in layers. Grouping comes first because brackets explicitly tell you what belongs together. Indices come next because powers are compact operations such as repeated multiplication. Multiplication and division come before addition and subtraction because they bind numbers more tightly in ordinary arithmetic and algebra. Finally, addition and subtraction combine the terms left over.

The Correct BIDMAS/BODMAS Order

The correct order is best understood as four levels, not six separate commands. Brackets are level 1. Indices or orders are level 2. Division and multiplication are level 3 together. Addition and subtraction are level 4 together. When operations are on the same level, move left to right.

A Simple Method for Solving Any BIDMAS Question

Many students know the acronym but still make mistakes because they try to do too much at once. The safest method is to scan the expression, mark the highest-priority operation that remains, complete only that step, rewrite the whole expression neatly, and repeat. Rewriting may feel slow, but it prevents mistakes in exams because every line shows exactly what changed.

Use this five-step method for any expression:

1. Circle or identify grouped parts. Look for brackets, fraction bars, roots, absolute value bars or other grouping symbols.
2. Simplify the grouped parts. If there are brackets inside brackets, start with the innermost brackets.
3. Evaluate powers and roots. Deal with exponents, square roots and cube roots after brackets.
4. Move left to right through division and multiplication. Do not skip over an earlier division to do a later multiplication.
5. Move left to right through addition and subtraction. Keep negative signs attached to their numbers.

Here is a small example: 6 + 3 x (8 - 5)^2. First calculate the bracket: 8 - 5 = 3, so the expression becomes 6 + 3 x 3^2. Next calculate the index: 3^2 = 9, so it becomes 6 + 3 x 9. Next multiply: 3 x 9 = 27. Finally add: 6 + 27 = 33. The answer is 33.

Notice that the expression was rewritten after each step. This is the easiest way to find errors. If your final answer is wrong, you can go back line by line and find the exact place where the rule was broken.

Brackets: The First Priority

Brackets tell you what to calculate first. They are the strongest instruction in the expression. In ordinary arithmetic, 2 + 3 x 4 equals 14, but (2 + 3) x 4 equals 20. The only difference is the bracket. The bracket changes the grouping and therefore changes the answer.

Nested brackets need a clear approach. Work from the inside outward. For example, in 2 x [7 + (9 - 4)], the innermost bracket is (9 - 4), which is 5. The expression becomes 2 x [7 + 5]. Then calculate the square bracket: 7 + 5 = 12. Finally multiply: 2 x 12 = 24.

Brackets can also be invisible. A fraction bar groups the numerator and denominator. The expression (2 + 6) / (1 + 3) is often written as a vertical fraction with 2 + 6 on top and 1 + 3 underneath. That fraction bar acts like brackets around the top and bottom. You simplify the numerator and denominator before dividing.

Roots also create grouping. In sqrt(9 + 16), the root applies to the whole expression under the sign, so you do 9 + 16 = 25, then sqrt(25) = 5. If the expression is written as sqrt(9) + 16, only the 9 is inside the root, so the answer is 3 + 16 = 19.

Indices, Orders, Powers and Roots

In BIDMAS, the I stands for indices. In BODMAS, the O stands for orders. Both words refer to powers and roots. A power such as 4^3 means 4 x 4 x 4, which is 64. A square root such as sqrt(81) asks for the number that squares to 81, which is 9.

Indices come after brackets but before ordinary multiplication and division. This is why 2 x 3^2 is 2 x 9 = 18, not 6^2 = 36. If the writer wanted 36, the expression should be written as (2 x 3)^2. Again, brackets control grouping.

Negative numbers with powers need special attention. (-4)^2 means (-4) x (-4), which is 16. But -4^2 is usually interpreted as -(4^2), which is -16. The brackets decide whether the negative sign is part of the base being squared.

Fractional powers and roots follow the same priority. In 5 + 16^(1/2) x 3, the fractional power means square root, so 16^(1/2) = 4. Then multiply: 4 x 3 = 12. Then add: 5 + 12 = 17. The order is unchanged even though the notation looks more advanced.

Division and Multiplication: Equal Priority, Left to Right

The most common BIDMAS misconception is the belief that division must always be completed before multiplication because D appears before M in the acronym. That is false. Division and multiplication are inverse operations at the same priority level. When they appear together, work from left to right.

The same rule applies when multiplication comes first. In 5 x 12 / 3, multiply first because it appears first: 5 x 12 = 60, then 60 / 3 = 20. You do not move the division forward simply because the acronym says D before M.

This rule is especially important when reading internet math puzzles. Many viral puzzles are written ambiguously or rely on people misunderstanding left-to-right rules. In school mathematics, the safest interpretation is always the standard convention unless the expression is genuinely unclear. When writing your own work, use brackets to remove doubt.

Addition and Subtraction: Equal Priority, Left to Right

Addition and subtraction also have equal priority. The acronym does not mean addition always comes before subtraction. In 20 - 8 + 5, you subtract first because the subtraction appears first. 20 - 8 = 12, then 12 + 5 = 17. The answer is 17.

If you add first, you get 20 - 13 = 7, which is wrong for the original expression. It would only be correct if the expression were 20 - (8 + 5). Once again, brackets decide a different grouping.

One useful mental model is to treat subtraction as adding a negative number. The expression 20 - 8 + 5 can be read as 20 + (-8) + 5. Addition can be rearranged, but students should be careful when they are still learning. For ordinary BIDMAS questions, left-to-right is safer and more transparent.

When expressions include several positive and negative terms, keeping signs attached is essential. In 7 - 12 + 4 - 3, work left to right: 7 - 12 = -5, then -5 + 4 = -1, then -1 - 3 = -4. The answer is -4.

Fractions, Fraction Bars and BIDMAS

Fractions are one of the places where invisible brackets matter most. A fraction bar groups the numerator and the denominator. If you see (3 + 5) / (2 + 2), you simplify the top and bottom before dividing. The numerator is 8. The denominator is 4. The result is 8 / 4 = 2.

If the same expression is typed on one line without brackets as 3 + 5 / 2 + 2, the meaning is different. Division happens before addition, so you do 5 / 2 = 2.5, then 3 + 2.5 + 2 = 7.5. This is why typed fractions need brackets when the numerator or denominator has more than one term.

When entering fractions into a calculator, use brackets generously. Type (3 + 5) / (2 + 2), not 3 + 5 / 2 + 2, if you mean the whole top divided by the whole bottom. This habit prevents many calculator errors in GCSE, IGCSE, IB, SAT, ACT, AP and everyday maths work.

Fractions also connect to algebra. The expression (x + 4) / 2 means the whole expression x + 4 divided by 2. But x + 4 / 2 means x + 2. That difference is huge when solving equations or simplifying formulae.

BIDMAS in Algebra

BIDMAS is not only for arithmetic. Algebra uses the same order of operations. In fact, algebra becomes much easier when you think of expressions as grouped terms. A term is a part of an expression connected by multiplication, division, powers or grouping before addition and subtraction combine it with other terms.

Consider 2x + 3x^2 when x = 4. Substitute first with brackets where needed: 2(4) + 3(4)^2. The power comes before multiplication: (4)^2 = 16. Then multiply: 2(4) = 8 and 3(16) = 48. Finally add: 8 + 48 = 56.

Now compare (2x + 3x)^2 when x = 4. Inside the bracket, 2x + 3x = 5x, so the expression becomes (5x)^2. Substituting gives (20)^2 = 400. This is very different from 2x + 3x^2. The bracket changed the structure.

When simplifying algebra, exponents usually apply only to the base they are attached to. 3x^2 means 3 x x^2, not (3x)^2. If you square both the coefficient and the variable, the expression must be written as (3x)^2, which equals 9x^2. This is a classic exam mistake.

BIDMAS on Calculators, Spreadsheets and Computers

Modern scientific calculators, spreadsheet programs and programming languages generally follow the standard order of operations, but they can only follow the expression you type. If you type an unclear expression, the technology may still give an answer, but it may not be the answer you intended.

In spreadsheets such as Excel or Google Sheets, formulas use ordinary operator precedence. Exponents, multiplication and division, then addition and subtraction are evaluated according to the program rules. If you want to calculate a percentage change, type the grouping clearly. For example, =(new-old)/old is different from =new-old/old. The first subtracts first, then divides. The second divides old/old first, then subtracts from new.

In programming, order of operations is also built into expressions. A JavaScript, Python or C-style expression such as 3 + 4 * 5 gives 23 because multiplication happens before addition. Programmers still use brackets because readability matters. Code that is mathematically correct but hard to read can create bugs.

For school calculators, the safest rule is: if an expression has a fraction, a negative base, a root, nested brackets or a long numerator, type extra brackets. Do not rely on memory. Check the display before pressing equals. A calculator is a tool, not a substitute for understanding.

Worked BIDMAS/BODMAS Examples

The examples below move from basic to exam-style. Read the reasoning, not just the answer. The goal is to train the habit of asking, "What is the highest-priority operation that remains?"

Common BIDMAS/BODMAS Mistakes

Most BIDMAS errors are predictable. Once you know the common traps, you can check for them quickly in your own work.

Exam Tips for BIDMAS/BODMAS Questions

Order of operations questions often look easy, which is exactly why students drop marks on them. The expression may be short, but it tests accuracy. In exams, accuracy beats speed. A student who rushes and misses a left-to-right step can lose a mark on a question they understood.

• Rewrite after each step. Do not try to hold three changes in your head at once.
• Mark equal-priority operations. If you see division and multiplication together, remind yourself to work left to right.
• Use brackets in substitution. When replacing x with a negative number, write brackets around the negative value.
• Check fraction grouping. In a vertical fraction, simplify the numerator and denominator separately.
• Be careful with calculator entry. If your working shows brackets but your calculator entry does not, the calculator may calculate a different expression.
• Do a reasonableness check. If an answer is extremely large or small, check whether a bracket or exponent was mishandled.
• Practice without a calculator. Many exam questions are designed to test understanding, not calculator speed.

BIDMAS/BODMAS Practice Questions With Answers

Try the questions first without looking at the answers. Then check the worked answer summary. If you get one wrong, identify the exact rule you missed.

BIDMAS in Word Problems and Real-Life Calculations

Order of operations is not just a classroom rule. It appears whenever a real problem is translated into a mathematical expression. If the expression is written incorrectly, the answer may be wrong even if the arithmetic is accurate.

Suppose a shop sells notebooks for 3 dollars each and charges a 4 dollar delivery fee. If you buy 6 notebooks, the total is 3 x 6 + 4, not 3 x (6 + 4). BIDMAS gives 18 + 4 = 22. The expression with brackets gives 30, which would mean the shop charges for 10 notebooks. The bracket changes the story.

In science, a formula such as s = ut + 0.5at^2 depends on correct order. If u = 3, t = 4, and a = 2, then ut = 3 x 4 = 12, t^2 = 16, and 0.5at^2 = 0.5 x 2 x 16 = 16. The total is 28. Squaring the wrong part of the expression would change the physics.

In finance, percentages need grouping. A price rises from 80 dollars to 100 dollars. The percentage increase is (100 - 80) / 80 x 100. The bracket tells you to find the change first. Without the bracket, 100 - 80 / 80 x 100 would be interpreted very differently and would not represent percentage increase.

In coding and spreadsheets, a formula can run thousands of times. A missing bracket may not just cause one wrong answer; it can cause a whole report, model or calculation sheet to be wrong. That is why BIDMAS is a foundational skill for mathematics, computing, engineering, business and data work.

More Worked Examples: From Easy to Exam-Ready

Once you understand the rule, the next step is fluency. Fluency means you can look at an expression, identify the first correct operation, and avoid being distracted by the operation that appears first on the page. The following examples are written in a slow style on purpose. In an exam you may not need this much explanation, but during revision it helps to see exactly why each step is chosen.

These pairs show a pattern: many BIDMAS questions are really grouping questions. If two expressions contain the same numbers but different brackets, they may have different meanings. When revising, do not only ask "What operations are present?" Ask "What is grouped with what?" That question will save marks in arithmetic, algebra, fractions and calculator work.

BIDMAS by Level: What Students Should Master

BIDMAS appears at different levels of mathematics, but the expectation changes as students move up. Younger students usually need to know that multiplication comes before addition. Older students must handle indices, negative numbers, algebraic substitution, roots, fractional expressions and calculator input. The same rule grows with the course.

For primary and early secondary students, the most valuable practice is short, repeated comparison: one expression with brackets and one without. For GCSE and IGCSE students, the key is combining BIDMAS with negative numbers, fractions and algebra. For IB, AP and A-level students, BIDMAS becomes part of bigger skills such as rearranging formulae, using functions, differentiating expressions or entering exact values into technology.

Teachers sometimes avoid saying "BIDMAS is a rule" because students can treat it as a chant instead of a system. A better phrase is "BIDMAS is a priority list." Brackets have the highest priority. Powers have the next priority. Multiplication and division share a priority. Addition and subtraction share the final priority. This language helps students understand why the equal-priority levels are left to right.

Ambiguous Expressions: Why Good Notation Matters

Sometimes students see arguments online about expressions such as 6 / 2(1 + 2). The disagreement usually comes from poor notation. According to a strict left-to-right interpretation after brackets, the expression becomes 6 / 2 x 3, which gives 9. But many people read the written form 2(1 + 2) as a tightly grouped denominator, giving 6 / [2(3)] = 1. The problem is not that mathematics is broken. The problem is that the expression is written unclearly.

In formal mathematics, the solution is to write what you mean. If the intended expression is 9, write (6 / 2)(1 + 2) or 6 / 2 x (1 + 2). If the intended expression is 1, write 6 / [2(1 + 2)]. Clear grouping removes the argument.

This matters in exams too. Most school exam boards avoid intentionally ambiguous one-line expressions, but students can create ambiguity in their own working. If your answer depends on a numerator or denominator with multiple terms, use brackets. If a negative value is being squared, use brackets. If a calculator entry has more than one operation in the top or bottom of a fraction, use brackets.

A useful rule is: if someone could reasonably read your expression two ways, rewrite it. Good mathematical writing is not about using the fewest symbols. It is about communicating structure. Brackets are part of that communication.

BIDMAS Revision Checklist

Use this checklist before a quiz, test or exam. You should be able to answer yes to each item. If one item feels weak, return to the relevant section above and practise that skill directly.

Challenge Practice: Mixed BIDMAS Questions

The following questions combine several ideas. Work them out on paper before reading the answers. For each question, write the reason for your first step. If you cannot explain why your first step is allowed, slow down and identify the highest-priority operation.

The final two questions are included to teach notation, not to start an argument. If a written expression could be read as two different structures, the best mathematical response is to rewrite it with brackets. In exams and professional work, clarity is more valuable than cleverness.

Teaching BIDMAS: How to Make the Rule Stick

For teachers, tutors and parents, the biggest challenge is moving students beyond chanting the acronym. A student can recite BIDMAS and still get 24 / 3 x 2 wrong. The teaching target should be conceptual: operations have priority levels, and equal-priority operations are completed left to right.

Start with contrasting pairs. Show 3 + 4 x 5 beside (3 + 4) x 5. Ask students why the answers differ. Then show 24 / 3 x 2 beside 24 / (3 x 2). These pairs teach that brackets are not decoration; they change meaning.

Use error analysis. Give students a wrong solution and ask them to find the first incorrect step. This builds mathematical judgment. For example, show 10 - 4 + 2 = 10 - 6 = 4. Students should explain that addition and subtraction have equal priority, so the correct first step is 10 - 4 = 6.

Finally, connect BIDMAS to calculators. Ask students to type the same expression with and without brackets. Let them see how a small change in input produces a different output. This builds the habit of writing clear mathematical expressions, not just following a rule mechanically.

BIDMAS/BODMAS Summary

• BIDMAS and BODMAS are memory aids for the order of operations.
• BIDMAS means Brackets, Indices, Division/Multiplication, Addition/Subtraction.
• BODMAS means Brackets, Orders, Division/Multiplication, Addition/Subtraction.
• PEMDAS is the same idea using Parentheses and Exponents.
• Brackets are completed first, including nested brackets and invisible grouping in fractions.
• Indices, orders, powers and roots are completed next.
• Division and multiplication have equal priority and are completed left to right.
• Addition and subtraction have equal priority and are completed left to right.
• Negative numbers and powers need brackets when the negative sign is part of the base.
• Calculators follow typed input, so use brackets to show exactly what you mean.

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