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Unary Operation — Definition, Formula & Examples

A unary operation is a math operation that acts on just one number to produce a result. Common examples include negation (making a number negative), taking the absolute value, and finding a square root.

A unary operation is a function that maps a single element from a set to another element, requiring exactly one operand. This distinguishes it from binary operations such as addition or multiplication, which require two operands.

How It Works

Whenever you apply an operation to a single number, you are using a unary operation. For example, writing −5-5 applies the negation operator to 55. Writing ∣−7∣|{-7}| applies the absolute value operator to −7-7. In contrast, 3+43 + 4 is a binary operation because it combines two numbers. The key test is simple: count how many inputs the operation needs. If it needs one, it is unary.

Worked Example

Problem: Identify the unary operations applied in the expression −∣−12∣-|{-12}|.
Step 1: Start with the innermost operation. The absolute value acts on −12-12, which is one input.
∣−12∣=12|{-12}| = 12
Step 2: Next, the negation operator acts on the result 1212, which is again one input.
−(12)=−12-(12) = -12
Answer: Two unary operations were applied: first absolute value, then negation. The final result is −12-12.

Why It Matters

Recognizing unary vs. binary operations helps you read mathematical notation correctly and follow the order of operations. In algebra, misreading a negation sign as subtraction (or vice versa) is a frequent source of errors that this distinction clears up.

Common Mistakes

Mistake: Confusing the negation sign (unary) with the subtraction sign (binary).
Correction: In −5-5, the minus sign is a unary operator acting on 55 alone. In 8−58 - 5, the minus sign is a binary operator combining 88 and 55. Context determines which one it is.