This page explains the division in first principles as splitting of a quantity, with examples in count or measure of quantities and in the number-line.

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There are `12` cars given to `4` showrooms. Each get equal number of cars.

Each showroom gets `3` cars.

Considering the figure with `12` cars and `4` boxes representing each of the `4` show rooms. `12` is split into `4` equal parts and one part is selected. And the counting is done from `1` to `3`. The resulting count is `3`.

A pencil is `12` centimeters in length. If the pencil is cut into `4` equal pieces, each piece is of length `3` centimeters.

A pencil is `12` centimeters in length. The pencil is split into `4` equal pieces and one piece is selected. The selected piece is measured to be `3` centimeter long.

The count or measure of quantities can be split into equal parts or *divided*.

The *division* results in the count or measure of one part of the quantity.

Division `12-:4` is given in number-line. The whole `12` is split into `4` equal parts. One part is chosen. The rest are grayed in the figure. The chosen part is counted in the number-line to be `3`.

The word "division" means: action of separating or splitting something.

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division

There are `11` cars given equally among `4` showrooms. Each showroom gets `2`, and `3` cars cannot be distributed.

Considering the figure with `11` cars and `4` dotted-boxes representing each of the `4` show rooms. `11` is split into `4` equal parts with each assigned `2` cars. There are `3` cars remaining. The remaining cars are not enough to assign equally to each dotted-box.

After distributing, one part is counted as `2` and remaining amount is `3`.

Division `11-:4` is given in number-line. The whole `11` is split into `4` equal parts with `3` remaining.

One part is chosen. The rest are grayed in the figure. The chosen part is counted in the number-line to be `2`.

**Division - First Principles** : Two numbers are considered, each of which represents a count or measurement. One of the amount is split into a number of parts given by the second. The amount of one part is the result.

eg: `11 -: 4 = 2` count and `3` remaining

`11` is the dividend

`4` is the divisor

`2` is the quotient

`3` is the remainder

`11-:4 = 2 text( quotient ) & 3 text( remainder )`

The word "dividend" means: a number that is being divided.

*familiarize with the terminology *

dividend

The word "divisor" means: a number that divides another number.

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divisor

The word "quotient" means: the result of a division.

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quotient

The word "remainder" means: the number left over in division.

*familiarize with the terminology *

remainder

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