Mathematical Operation — Definition, Formula & Examples
A mathematical operation is a process that takes one or more numbers and produces a new result. The four basic operations are addition, subtraction, multiplication, and division.
A mathematical operation is a rule that assigns to one or more input values (called operands) a unique output value. In elementary arithmetic, the binary operations addition (+), subtraction (−), multiplication (×), and division (÷) each combine two operands to produce a single result, while unary operations such as negation act on a single operand.
How It Works
You use mathematical operations every time you combine numbers to get a new number. Each operation has its own symbol: + for addition, − for subtraction, × for multiplication, and ÷ for division. The numbers you start with are called operands, and the number you get after performing the operation is called the result. For example, in , the operation is addition, the operands are 3 and 5, and the result is 8. When a problem has more than one operation, you follow the order of operations (PEMDAS) to decide which to do first.
Worked Example
Problem: Identify each operation and find the result: 12 + 5, then 12 × 5, then 60 ÷ 5, then 12 − 5.
Addition: Add 12 and 5.
Multiplication: Multiply 12 by 5.
Division: Divide 60 by 5.
Subtraction: Subtract 5 from 12.
Answer: The four results are 17, 60, 12, and 7. Each came from a different mathematical operation applied to the operands.
Another Example
Problem: Evaluate the expression using the correct order of operations.
Step 1: There are two operations: addition and multiplication. Multiplication comes first in the order of operations.
Step 2: Now perform the addition with the result from Step 1.
Answer: The value of is .
Why It Matters
Understanding mathematical operations is the foundation of every math course from elementary arithmetic through algebra and beyond. When you solve word problems — like figuring out the total cost of 6 items at $4 each — you are choosing and applying the right operation. Careers in engineering, finance, and computer science all rely on selecting and combining operations correctly.
Common Mistakes
Mistake: Performing operations from left to right without following the order of operations.
Correction: When an expression contains more than one operation, always do multiplication and division before addition and subtraction (unless parentheses change the order). For example, , not .
Mistake: Confusing the operation with its result — for instance, calling the answer to a subtraction problem a "product."
Correction: Each operation has its own name for the result: addition gives a sum, subtraction gives a difference, multiplication gives a product, and division gives a quotient.