# Multiplication

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**Multiplication**, usually denoted by the symbol × or ·, is a fundamental operation that is defined differently for different mathematical objects.

In arithmetic, **multiplication** of natural numbers can be defined in terms of repeated addition. That definition can easily be extended to rational, real and complex numbers.

In abstract algebra, multiplication is an operation that isn't always explicitly defined, but rather is assumed to satisfy some axioms. For example:

- In multiplicative groups, multiplication is assumed to be associative, have an identity element, and that each group element has an inverse.
- In rings, which also have an addition operation, multiplication is assumed to be associative and distributive over addition.
- In commutative rings, multiplication is assumed to be commutative.
- In integral domains, multiplication is assumed to satisfy the zero-product rule.
- In rings with unity, there exists a multiplicative identity.
- Fields are commutative rings with unity in which every element except 0 (the additive identity) have multiplicative inverses.

Other objects, such as vectors, quaternions and matrices have their own definitions of multiplication.

## Answers

The answer to a multiplication problem is the product.

## In Real Life

Multiplication is widely used in real life as in converting currencies, computing total salaries, and many others.

## Estimation

It is possible to estimate a product to round the multiplicands and the multipliers to several significant figures then multiply the rounded numbers.

## Applications

If a integer is multiplied by the other integer, the first integer is continuously doubled until the second integer continuously decreased until 1, as follows: