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Thought-Process to Discover Knowledge

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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

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### Division: First Principles

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.

familiarize with the terminology
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.

familiarize with the terminology
divisor

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

familiarize with the terminology
quotient

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

familiarize with the terminology
remainder

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