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Operations
Properties and precedence of operators
5
Mathematics
Undergraduate 1
08/09/2020

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Term

Binary Operation

Definition

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.
Term

Unary Operation

Definition

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)...
Term

Commutativity

Definition

Definition

Definition: a calculation where changing the order of inputs does not change the result.

 

Commutative   Not Commutative
y = y + x yy - x
× b = b × a ÷ bb ÷ a
(ab)c(ac)b  
Term

Associativity

Definition

Definition

Definition: a series of operations where order can be altered but leave the result unchanged.

 

Associative   Not Associative
(x + y) + z = x + (y + z) (x - y) - z ≠ x - (y - z)
(a × b) × c =  × (b × c)
(a ÷ b) ÷ c ≠  ÷ (b ÷ c)
  a(bc) ≠ (ab)c 
Term

Order of Operations

Definition

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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