In mathematics, division is an arithmetic operation that is no doubt, a widely using operation in daily life. Without division, it is truly impossible to run the circle of life either in any field. Basically, there are three major components of any division that are dividend, divisor and quotient. However, division is not as simple as looks like the combination of these three parts. There are many hidden facts about division. Let’s take a look on these mysterious facts.
1. Division by Zero
The result of any such mathematical figure that would be divisible by zero is still undefined.
2. Division of Real Numbers
The result of dividing two real numbers will be also a real number nothing else. The only result is that the divisor should not be zero.
3. Division of Integers
Division of integers is not closed. Apart from division by zero being undefined, the quotient will not be an integer unless the dividend is an integer multiple of the divisor; for example 26 cannot be divided by 10 to give an integer.
4. Division of Complex Numbers
The result of division in case of complex numbers is also a complex number again. The condition is still same, means the divisor should not be zero.
5. Division of Polynomials
The result of polynomial division is not so much different from integers as one has a reminder.
6. Division of Matrices
To understand clearly the concept of matrices division, let’s take an example. The usual way to do this is to define A / B = AB−1, where B−1 denotes the inverse of B, but it is far more common to write out AB−1 explicitly to avoid confusion.
7. Division by one
The result of any mathematical relation that is divisible by one, remain same or you can say unaffected.
8. Division Algorithm
The division Algorithm is a mathematical theorem that precisely expresses the outcome of the usual process of division of integers.
9. Left Division
A left division or backslash-division is defined as A \ B = A−1B. For this to be well defined, B−1 need not exist, however A−1 does need to exist.
10. Right Division
Right division or Slash Division is defined as A / B = AB−1