Maths Books

Basic operation

Basic Operations

The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.

In basic mathematics there are many ways of saying the same thing:


Calculate the sum, difference, product, and quotient of positive whole numbers.


Key Points

  • The basic arithmetic operations for real numbers are addition, subtraction, multiplication, and division.
  • The basic arithmetic properties are the commutative, associative, and distributive properties.

Key Terms

  • associative: Referring to a mathematical operation that yields the same result regardless of the grouping of the elements.
  • commutative: Referring to a binary operation in which changing the order of the operands does not change the result (e.g., addition and multiplication).
  • product: The result of multiplying two quantities.
  • quotient: The result of dividing one quantity by another.
  • sum: The result of adding two quantities
  • difference: The result of subtracting one quantity from another.

The Four Arithmetic Operations


Addition is the most basic operation of arithmetic. In its simplest form, addition combines two quantities into a single quantity, or sum. For example, say you have a group of 2 boxes and another group of 3 boxes. If you combine both groups together, you now have one group of 5 boxes. To represent this idea in mathematical terms:



Subtraction is the opposite of addition. Instead of adding quantities together, we are removing one quantity from another to find the difference between the two. Continuing the previous example, say you start with a group of 5 boxes. If you then remove 3 boxes from that group, you are left with 2 boxes. In mathematical terms:


Multiplication (×)

Multiplication also combines multiple quantities into a single quantity, called the product. In fact, multiplication can be thought of as a consolidation of many additions.


Division is the inverse of multiplication. Rather than multiplying quantities together to result in a larger value, you are splitting a quantity into a smaller value, called the quotient. Again, to return to the box example, splitting up a group of 8 boxes into 4 equal groups results in 4 groups of 2 boxes:

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