Term
Binary Operation
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Definition
Definition: a calculation that combines two elements to produce another element.
Examples:
- x+y, a-b, c×d, m÷n.
- Quantities such as +, -, ×, ÷ are called binary operators.
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Term
Unary Operation
Definition |
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Definition
Definition: a calculation that combines only one element/input to produce another element or output.
Examples:
- Negation: -x, -(-y) = y.
- Functions of one variable, e.g. sin(x), cos(α), tan(β)...
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Term
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Definition
Definition: a calculation where changing the order of inputs does not change the result.
| Commutative |
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Not Commutative |
| x + y = y + x |
x - y ≠ y - x |
| a × b = b × a |
a ÷ b ≠ b ÷ a |
| (ab)c = (ac)b |
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Term
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Definition
Definition: a series of operations where order can be altered but leave the result unchanged.
| Associative |
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Not Associative |
| (x + y) + z = x + (y + z) |
(x - y) - z ≠ x - (y - z) |
(a × b) × c = a × (b × c)
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(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)
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a(bc) ≠ (ab)c |
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Term
Order of Operations
Definition |
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Definition
Definition: order/precedence when evaluating an expression. Mnemonic: PEMDAS
- Parentheses
- Exponents
- Multiplication/Division, evaluated left to right
- Addition/Subtraction, evaluated left to right
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