How modulus works?

[dennisl]

Hi,

Good day to you.

I have been searching information about modulus for days but I found that they all gave different answers (from my opinion .....)

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$a % $b
Basically, the defination is the remainder when you divide $a by $b.

1) First example from website

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"what if you take 7/5? If you plug this into the PHP engine, you'll get a decimal number of 1.4. However, if you do 7 modulus 5, you're going to get 2."

I think I can understand this, the result is rounded up to the nearest integer to 2.

2) Second example from book.

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"27 % 10, answer is 7."

I failed to understand why 27 / 10 and the remainder is 7. Shouldn't it be 2.7 ? Even if it rounds to nearest integer, it should be 2 or 3.

3) Third exmaple from tizag

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"Perform modulus: 5 % 2 = 1. Modulus is the remainder after the division operation has been performed. In this case it was 5 / 2, which has a remainder of 1. "

Again, after dividing 5 by 2, it should be 2.5, how it becomes 1?

I wish to get some advice from you.
Thank you.

[Wiedmann]

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"27 % 10, answer is 7."

Modulo is defined as:

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(a mod m) = a - m * (a div m)

(the result of "a div m" is converted to an integer (round down to zero))

Example

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(27 mod 10) = 27 - 10 x (27 div 10)
(27 mod 10) = 27 - 10 x (2)          // 27 : 10 = 2.7; (int) 2.7 = 2
(27 mod 10) = 27 - 20
(27 mod 10) = 7

[glitzi85]

Or to make Wiedmann's Post short: You subtract the second number as often as possible from the first number. What remains is your result. Example:

27 mod 8:

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27 - 8 = 19
19 - 8 = 11
11 - 8 = 3

That means: 27 mod 8 = 3

glitzi