<<–2/”>a href=”https://exam.pscnotes.com/5653-2/”>h2>BIDMAS: The Order of Operations
BIDMAS is an acronym that stands for Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). It is a set of rules used to determine the order in which mathematical operations should be performed in a mathematical expression.
Why is BIDMAS Important?
Without a standard order of operations, the result of a mathematical expression could vary depending on who is solving it. For example, consider the expression:
2 + 3 x 4
If we perform the addition first, we get:
2 + 3 x 4 = 5 x 4 = 20
However, if we perform the multiplication first, we get:
2 + 3 x 4 = 2 + 12 = 14
BIDMAS ensures that everyone arrives at the same answer for a given expression.
Understanding the Rules
Here’s a breakdown of the rules in BIDMAS:
1. Brackets (Parentheses)
Any operations within brackets should be performed first.
2. Indices (Orders)
Indices, also known as exponents or powers, are calculated next.
3. Division and Multiplication
These operations are performed from left to right. This means that if a division operation appears before a multiplication operation in an expression, the division is performed first.
4. Addition and Subtraction
These operations are also performed from left to right.
Examples
Let’s illustrate the application of BIDMAS with some examples:
Example 1:
10 + 5 x 2 – 4 ÷ 2
- Multiplication: 5 x 2 = 10
- Division: 4 ÷ 2 = 2
- Addition: 10 + 10 = 20
- Subtraction: 20 – 2 = 18
Therefore, 10 + 5 x 2 – 4 ÷ 2 = 18
Example 2:
(3 + 2) x 4 – 6 ÷ 2
- Brackets: (3 + 2) = 5
- Multiplication: 5 x 4 = 20
- Division: 6 ÷ 2 = 3
- Subtraction: 20 – 3 = 17
Therefore, (3 + 2) x 4 – 6 ÷ 2 = 17
Example 3:
2² + 3 x 5 – 10 ÷ 2
- Indices: 2² = 4
- Multiplication: 3 x 5 = 15
- Division: 10 ÷ 2 = 5
- Addition: 4 + 15 = 19
- Subtraction: 19 – 5 = 14
Therefore, 2² + 3 x 5 – 10 ÷ 2 = 14
Alternative Acronyms
While BIDMAS is a widely used acronym, other variations exist, such as:
- BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction
- PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
These acronyms all represent the same order of operations.
Importance of BIDMAS in Real-Life
BIDMAS is not just a theoretical concept. It is essential for solving real-life problems involving calculations. For example:
- Finance: Calculating interest on loans or investments involves using BIDMAS to determine the order of operations.
- Engineering: Designing structures or machines requires accurate calculations, which rely on BIDMAS to ensure consistency.
- Science: Scientific experiments often involve complex calculations that require the use of BIDMAS to obtain accurate results.
Table 1: BIDMAS Rules Summary
| Order | Operation | Description |
|---|---|---|
| 1 | Brackets (Parentheses) | Perform operations within brackets first. |
| 2 | Indices (Orders) | Calculate exponents or powers. |
| 3 | Division and Multiplication | Perform these operations from left to right. |
| 4 | Addition and Subtraction | Perform these operations from left to right. |
Table 2: Examples of BIDMAS in Action
| Expression | Solution | Explanation |
|---|---|---|
| 5 + 2 x 3 | 11 | Multiplication before addition: 2 x 3 = 6, then 5 + 6 = 11 |
| (5 + 2) x 3 | 21 | Brackets first: (5 + 2) = 7, then 7 x 3 = 21 |
| 10 ÷ 2 + 5 | 10 | Division before addition: 10 ÷ 2 = 5, then 5 + 5 = 10 |
| 2² + 3 x 4 | 16 | Indices first: 2² = 4, then multiplication: 3 x 4 = 12, then addition: 4 + 12 = 16 |
Frequently Asked Questions
Q: What if there are multiple sets of brackets in an expression?
A: Work from the innermost set of brackets outwards.
Q: What if there are multiple division or multiplication operations in an expression?
A: Perform them from left to right.
Q: What if there are multiple addition or subtraction operations in an expression?
A: Perform them from left to right.
Q: Is there a way to remember BIDMAS?
A: Yes, there are several mnemonics that can help you remember the order of operations. Some popular ones include:
- Please Excuse My Dear Aunt Sally: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
- Big Elephants Dance And Sing Melodies: Brackets, Exponents, Division, Addition, Subtraction, Multiplication
Q: Why is BIDMAS important for programming?
A: In programming, the order of operations is crucial for ensuring that code executes correctly. Programming languages typically follow the same order of operations as BIDMAS.
Q: Can I use a calculator to help me with BIDMAS?
A: Most scientific calculators are programmed to follow BIDMAS. However, it’s important to understand the rules yourself so you can check the calculator’s results and avoid errors.
Q: Are there any exceptions to BIDMAS?
A: While BIDMAS is a general rule, there are some exceptions in specific mathematical contexts. For example, in some advanced mathematical operations, the order of operations may be different. However, for most everyday calculations, BIDMAS is the standard to follow.