(This explanation is only for positive numbers since it depends on the language otherwise)

**Definition**

The *Modulus* is the remainder of the euclidean division of one number by another. `%`

is called the *modulo operation*.

For instance, `9`

divided by `4`

equals `2`

but it remains `1`

. Here, `9 / 4 = 2`

and `9 % 4 = 1`

.

In your example: 5 divided by 7 gives 0 but it remains 5 (`5 % 7 == 5`

).

**Calculation**

The modulo operation can be calculated using this equation:

a % b = a - floor(a / b) * b

`floor(a / b)`

represents the number of times you can divide`a`

by`b`

`floor(a / b) * b`

is the amount that was successfully shared entirely- The total (
`a`

) minus what was shared equals the remainder of the division

Applied to the last example, this gives:

5 % 7 = 5 - floor(5 / 7) * 7 = 5

**Modular Arithmetic**

That said, your intuition was that it could be -2 and not 5. Actually, in modular arithmetic, `-2 = 5 (mod 7)`

because it exists k in Z such that `7k - 2 = 5`

.

You may not have learned modular arithmetic, but you have probably used angles and know that -90° is the same as 270° because it is modulo 360. It’s similar, it wraps! So take a circle, and say that it’s perimeter is 7. Then you read where is 5. And if you try with 10, it should be at 3 because `10 % 7`

is 3.