Java modulus concept - arithmetic definition (a/b)*b+(a%b)

Question

I have recently started learning code (Java), and have looked up the modulus operator on the Oracle website, as per the section 15.17.3. of the following link:

http://docs.oracle.com/javase/specs/jls/se8/html/jls-15.html#jls-15.17.3

Basically, if a is the denominator, and b is the nominator, it states that: (a/b) * b + (a%b) = a , which defines the modulus operator as: a%b = a – (a/b) * b .

I am confused because the equation simply does not work, which can be simplified as a%b = 0 . I know my basic math algebra, so I am hoping if someone can enlighten me on how is it supposed to equal?

Answer 1

For integers, operator / means integral division, not mathematical one, for example:

7/2 = 3
6/2 = 3
5/2 = 2
4/2 = 2
3/2 = 1
2/2 = 1
1/2 = 0

In math terms, formula from java spec will be written like:

⌊a/b⌋ * b + (a%b) = a
a%b = a – ⌊a/b⌋ * b