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 very 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: