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