How to Solve BODMAS Questions Step by Step
Arithmetic looks simple when dealing with two numbers, but confusion arises the moment multiple operations appear in a single mathematical problem. If you look at an expression like ten plus two multiplied by five, do you add first to get sixty, or multiply first to get twenty? Without rules, two people could solve the exact same equation and arrive at completely different results. To eliminate ambiguity, mathematicians rely on operational priority, and using an online solver confirms that your arithmetic follows these universal rules every time.
The standard acronym used across many schools to remember this sequence is BODMAS. Understanding what each letter represents gives you complete confidence when tackling multi-step math problems on tests, homework, or financial sheets.
What BODMAS Stands For
BODMAS is an acronym designed to help students remember the order in which mathematical operations must be evaluated. Each letter corresponds to a specific category of mathematical operation, arranged in descending order of priority.
- B stands for Brackets, encompassing round parentheses, square brackets, and curly braces.
- O stands for Orders, which refers to powers, exponents, indices, and square roots.
- D stands for Division, representing the division of numbers.
- M stands for Multiplication, representing the multiplication of quantities.
- A stands for Addition, combining positive quantities.
- S stands for Subtraction, taking away one quantity from another.
Why the Order Matters in Real Arithmetic
Mathematical operations do not carry equal weight because higher operations represent repeated forms of lower ones. Multiplication is repeated addition, and exponentiation is repeated multiplication. Evaluating operations out of sequence changes the underlying meaning of the problem.
Consider six plus four multiplied by three. Calculating from left to right without rules gives ten multiplied by three, or thirty. But mathematically, the four belongs to the three as four groups of three. Multiplying four by three first yields twelve, and adding six produces the true answer of eighteen.
The Hidden Left to Right Rule
A frequent misunderstanding involves the pairs Division and Multiplication, as well as Addition and Subtraction. Many learners assume that because D comes before M in the word BODMAS, division must always be executed before multiplication. In actual mathematics, Division and Multiplication share equal priority. The same holds true for Addition and Subtraction.
Also read: Understanding the Order of Operations in Math
You may also like: Simplifying Algebraic Expressions Step by Step
When operations of equal priority appear together without brackets, evaluate them strictly from left to right. For example, in the expression twenty divided by four multiplied by two, division and multiplication have equal ranking. You first calculate twenty divided by four to get five, then multiply five by two to get ten. If you multiplied four by two first, you would obtain twenty divided by eight, which produces an incorrect result of 2.5.
Step by Step Worked Examples
Working through problems of varying difficulty demonstrates how to apply each stage of the rule methodically. You can check your intermediate lines using an interactive caluculator to ensure no basic computational slip occurs.
Beginner Level Problem
Evaluate the expression: twenty-four minus three multiplied by five plus eight.
First, inspect the expression for brackets or exponents. Since none exist, locate multiplication and division. The multiplication three multiplied by five must be resolved first, producing fifteen. The expression now reads twenty-four minus fifteen plus eight. Now, evaluate addition and subtraction from left to right. Subtracting fifteen from twenty-four leaves nine. Finally, adding nine and eight produces seventeen as the finished solution.
Intermediate Level Problem with Brackets and Orders
Evaluate the expression: six multiplied by the quantity two cubed plus four, all divided by eight.
Begin inside the brackets. Inside the parentheses, you have two cubed plus four. The order or power must be computed before addition, so evaluate two cubed as eight. Now finish the bracket by adding eight and four, which equals twelve. The expression simplifies to six multiplied by twelve divided by eight. Moving from left to right through equal operations, six multiplied by twelve is seventy-two. Finally, seventy-two divided by eight yields nine.
Advanced Level Problem with Nested Brackets
Evaluate the expression: fifty minus square bracket twelve plus round bracket eight minus two multiplied by three round bracket squared square bracket.
Always start with the innermost grouping. Inside the round brackets, evaluate two multiplied by three first, which is six. Then subtract six from eight, leaving two. The expression inside the square brackets is now twelve plus two squared. Next, evaluate the exponent: two squared equals four. Add twelve and four to complete the square brackets, giving sixteen. Finally, subtract sixteen from fifty to reach thirty-four. Running complex multi-bracket questions through a reliable solver provides instant verification when studying alone.
| Priority Rank | Letter | Operation Type | Evaluation Rule | Mini Example |
|---|---|---|---|---|
| First | B | Brackets | Evaluate innermost groups first | (3 + 5) becomes 8 |
| Second | O | Orders | Compute powers, roots, and exponents | 4 squared becomes 16 |
| Third | D and M | Division and Multiplication | Equal rank, evaluate left to right | 12 / 3 * 2 becomes 8 |
| Fourth | A and S | Addition and Subtraction | Equal rank, evaluate left to right | 10 – 4 + 2 becomes 8 |
Common Pitfalls and How to Avoid Them
One common mistake is failing to write down each step. When you attempt to perform three operations mentally at once, numbers get mixed up. Writing down each successive simplified line of arithmetic keeps your working clear and easy to audit.
Another frequent trap is ignoring brackets when negative signs appear. If an expression contains minus the quantity four plus two, you must add four and two first to get six, making the final value negative six.
Summary
Solving multi-step math problems reliably comes down to respecting operational precedence. By addressing brackets first, resolving orders, handling division and multiplication from left to right, and concluding with addition and subtraction, you ensure that every calculation leads to the mathematically correct answer.
