To evaluate an expression using BODMAS, you must follow a specific order of operations to ensure you get the correct result. BODMAS is an acronym that stands for:
- Brackets
- Orders (powers and square roots, etc.)
- Division
- Multiplication
- Addition
- Subtraction
This order dictates the sequence in which operations should be performed in a mathematical expression.
Understanding the BODMAS Order
The BODMAS rule provides a clear hierarchy for evaluating mathematical expressions:
- Brackets: Any operation within brackets is always performed first, starting from the innermost brackets if multiple sets are present.
- Orders (Powers and Roots): Next, you evaluate any powers, roots, or indices.
- Division and Multiplication: After brackets and orders, proceed with division and multiplication, working from left to right in the expression.
- Addition and Subtraction: Finally, perform addition and subtraction, also working from left to right in the expression.
Practical Example
Let's consider an example to illustrate how BODMAS works:
2 + 3 * (6 - 4)^2 / 2
Here’s how we would solve this step-by-step using BODMAS:
- Brackets: First, we solve inside the bracket:
(6 - 4) = 2. The expression now becomes2 + 3 * 2^2 / 2. - Orders: Next, evaluate the power:
2^2 = 4. The expression now becomes2 + 3 * 4 / 2. - Division and Multiplication: Perform multiplication and division from left to right:
3 * 4 = 12.12 / 2 = 6.
The expression now becomes2 + 6.
- Addition and Subtraction: Perform the final addition:
2 + 6 = 8.
Therefore, the result of the expression 2 + 3 * (6 - 4)^2 / 2 is 8.
Summary of BODMAS
| Order | Operation | Example |
|---|---|---|
| 1 | Brackets | (1 + 2) |
| 2 | Orders | 2^3, √9 |
| 3 | Division | 6 / 3 |
| 4 | Multiplication | 4 * 2 |
| 5 | Addition | 5 + 1 |
| 6 | Subtraction | 7 - 2 |
By consistently applying the BODMAS rule, you can ensure that mathematical expressions are evaluated correctly and avoid calculation errors. Remember to always work from left to right when performing operations with the same precedence, such as division and multiplication, or addition and subtraction.
