The rule for division, multiplication, addition, and subtraction is that they must be performed in a specific order called the order of operations.
Understanding the Order of Operations
The order of operations ensures that mathematical expressions are evaluated consistently, preventing ambiguity. The established rule dictates:
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Multiplication and Division: These operations are performed before addition and subtraction.
- When both multiplication and division are present, they are executed from left to right.
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Addition and Subtraction: These are performed after multiplication and division.
- When both addition and subtraction are present, they are executed from left to right.
PEMDAS/BODMAS
You might encounter acronyms like PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) to remember this order. These acronyms help you remember the correct sequence. They both essentially represent the same rules, but with different naming conventions.
Examples
Let's look at how these rules apply in practice:
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Example 1: 10 + 5 x 2
- First, do the multiplication: 5 x 2 = 10
- Then, do the addition: 10 + 10 = 20
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Example 2: 20 / 4 - 3 + 7
- First, do the division: 20 / 4 = 5
- Then, do the subtraction and addition from left to right: 5 - 3 = 2
- Finally, 2 + 7 = 9
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Example 3: 12 - 2 x 3 + 8 / 2
- Multiplication and Division from left to right: 2 x 3 = 6 and 8 / 2 = 4
- The equation becomes: 12 - 6 + 4
- Subtraction and addition from left to right: 12 - 6 = 6 and 6 + 4 = 10
Summary
The order of operations ensures that mathematical calculations are consistent. Remember to always perform multiplication and division from left to right before addition and subtraction from left to right.
| Order | Operation |
|---|---|
| 1 | Multiplication and Division (Left to right) |
| 2 | Addition and Subtraction (Left to right) |
