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 result from multiplying two numbers together is called the product.
In Real Life
Multiplication is widely used in real life in economics, or in most areas of physics.
It is possible to estimate a product by rounding the multiplicands and the multipliers to fewer significant figures, then multiplying the rounded numbers.
If two integers, are multiplied together, the product is the sum of . times, or equivalently the sum of , times. Written out in standard notation this is