In long division we have four parts to the overall expression.

```
Dividend => the number being divided
Divisor => the number being divided by
Quotient => the whole number result
Remainder => the non-divisible amount
```

Take `11`

over `3`

from your example…

```
11 / 3 => 3.66..
```

but when we take `0.66..`

and resolve it to a rational number (all repeating decimals are rational numbers) we get `2/3`

.

Now multiply `2/3`

by the divisor, `3`

, and we get `2`

. Thus, 11 modulo 3 is 2.

```
11 % 3 => 2
```

Now consider the whole number quotient, `3`

,

```
3 * 3 => 9
11 - 9 => 2
```

Again, remainder of 2.

We can use the remainder as a signal of non-divisibility. If the remainder is not zero, then the dividend cannot be divided evenly by the divisor. We now know with certainty that 3 does not divide into 11. There will always be a remainder.

From what we’ve covered above we have a simple formula…

```
D - qd = R
```

D is the Dividend; d is the divisor; q is the quotient; and, R is the remainder. This holds for integers or floats though in JavaScript, float remainders are not supported. We must look at this from the integer perspective.