How Does BIDMAS Work?
BIDMAS is an acronym used to remember the order of operations in mathematics. It stands for Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This order ensures everyone arrives at the same answer when solving a mathematical expression.
The key to BIDMAS is performing operations in the correct sequence:
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Brackets (or Parentheses): Always solve anything inside brackets first. This isolates parts of the equation and prevents ambiguity. A horizontal fraction line acts like brackets, with the numerator and denominator treated separately.
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Indices (or Orders/Powers/Roots): Next, calculate any exponents or roots.
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Division and Multiplication: These operations have equal precedence. Perform them from left to right as they appear in the expression.
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Addition and Subtraction: Similar to division and multiplication, these have equal precedence and are solved from left to right.
Examples Illustrating BIDMAS
Let's illustrate with a few examples:
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Example 1: 10 + 5 × 2 = ?
Following BIDMAS:
- Multiplication first: 5 × 2 = 10
- Addition next: 10 + 10 = 20
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Example 2: (10 + 5) × 2 = ?
Following BIDMAS:
- Brackets first: 10 + 5 = 15
- Multiplication next: 15 × 2 = 30
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Example 3: 12 ÷ 3 × 2 + 4 – 1 = ?
Following BIDMAS:
- Division first (from left to right): 12 ÷ 3 = 4
- Multiplication next (from left to right): 4 × 2 = 8
- Addition next (from left to right): 8 + 4 = 12
- Subtraction last: 12 – 1 = 11
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Example 4 (Fractions): (2 + 3)/5 + 1 =?
The fraction line acts like brackets. Therefore the addition in the numerator is calculated first.
- Brackets (numerator): 2 + 3 = 5
- Division: 5/5 = 1
- Addition: 1 + 1 = 2
Why BIDMAS Works
BIDMAS isn't arbitrary; it's based on the fundamental structure of mathematical notation. It allows us to write complex polynomial expressions concisely without needing excessive parentheses. By agreeing on a standard order of operations, everyone interprets the same mathematical expression identically.
