(KS2, Year 4)

An operation takes values and calculates a new value from them.

Dictionary Definition

The Merriam-Webster dictionary defines an operation as "any of various mathematical or logical processes (such as addition) of deriving one entity from others according to a rule. Multiplication is one mathematical operation."

The Basic Operations

The most common operations take two values and calculates a new value from them. The basic operations in arithmetic are:
  • Addition +.
  • Subtraction .
  • Multiplication ×.
  • Division ÷.


Takes two numbers and adds them together.

operations add


Takes two numbers and subtracts the number on the right from the number on the left.

operations subtract


Takes two numbers and multiplies them.

operations multiply


Takes two numbers and divides the number on the left by the number on the right.

operations divide

Lesson Slides

The slider below shows more about operations.

More Operations

Some operations take one value and calculates a new value from them.
  • Exponents
  • Negation
  • Reciprocal


An exponent tells you how many times a number (or other quantity) is multiplied by itself.


For example, an exponent of 2 means squaring a number.

operations square The opposite of squaring a number is finding the square root.

Square Root

An exponent of 12 means finding the square root of a number. The square root of a number, when multiplied by itself, gives that number.

operations square root


Negation finds the negative value of a number. For example, negating 2 produces −2.

operations negation


The reciprocal of a number is the result of dividing 1 by that number. For example, the reciprocal of 2 is calculated by dividing 1 by 2.

operations reciprocal

The Parts of Operations

parts of operations explained
  • The numbers operated upon are called operands.
  • The symbol which shows what type of operation is taking place is called the operator.

The Arity of Operations

The arity of operations is given by how many operands there are. The most common operations are binary operations, which have an arity of 2. There are 2 operands. Addition is a binary operation:
2 + 3 → 5
A unary operation has an arity of 1. There is only 1 operand. Negation is a unary operation:
−(2) → −2
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This page was written by Stephen Clarke.

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