The rules governing addition, subtraction, multiplication, and division, especially when combined in a single expression, follow a specific order of operations, often remembered by acronyms like PEMDAS or BODMAS. This ensures consistent results. Here's a breakdown:
Order of Operations
The fundamental rule is that multiplication and division take precedence over addition and subtraction. This is crucial for getting the correct answer in a mathematical expression.
Ranking
Here's a quick table summarizing the order:
| Rank | Operation |
|---|---|
| 1 | Multiplication & Division |
| 2 | Addition & Subtraction |
Detailed Rules
- Multiplication and Division Have Equal Rank: This means they are treated with the same priority.
- Left-to-Right Rule: When multiplication and division appear consecutively in an expression, they are solved from left to right.
- Example: In
10 / 2 * 3, we divide 10 by 2 first, getting 5, then multiply by 3, resulting in 15.
- Example: In
- Division as Multiplication: An alternative way to handle consecutive multiplication and division is to treat division as multiplication by the reciprocal. For instance,
10 / 2 * 3is the same as10 * (1/2) * 3. This might make it easier for complex calculations where multiple divisions appear.
Examples:
- Example 1:
10 + 5 * 2: Here, we multiply 5 * 2 first (resulting in 10), then we add 10, giving us a final answer of 20.
- Example 2:
20 - 10 / 2: Here, we divide 10 by 2 first (resulting in 5), then subtract that from 20, giving us an answer of 15.
- Example 3:
3 * 5 / 3 + 7 - 2: Following the left-to-right rule for multiplication and division, and then addition and subtraction also from left to right we get the following:15 / 3 + 7 - 2->5 + 7 - 2->12 - 2->10.
Key Points
- Always solve multiplication and division before addition and subtraction.
- Work from left to right for operations with equal precedence.
- Treating division as multiplication with the reciprocal is also a method to solve for these operations.
By adhering to these rules, calculations involving addition, subtraction, multiplication, and division will produce the correct and consistent results.
