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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

Read in the blogs more about the unique learning experience at nubtrek.
mathsWhole NumbersWhole Numbers: Multiplication and Division

### Multiplication: First Principles

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

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3 cars were given to 4 show rooms each. How many cars were given in total?

• 3+4=7
• 3+3+3+3=12
• 3+3+3+3=12

The answer is '12'. The problem is understood to be that of repeated addition.

3 cars were given to the first show room, then to the second, then to the third, and then to the fourth. So 3 was repeatedly added 4 times to get the total.

Considering 3 cars given to 4 show rooms each. All the cars are shown in the figure. Counting the number of cars, the result is 12.

There are 4 pencils, each of 3 centimeter long. What is the combined length of the 4 pencils?

• 4+3=7
• 3+3+3+3=12
• 3+3+3+3=12

The answer is '12'. The problem is understood to be that of repeated addition.

Length of one pencil is 3 centimeters. To get the combined length of 4 such pencils, the length is repeatedly added 4 times.

Considering 4 pencils, each of 3 centimeter long. The four pencils are placed side-by-side and the length measurement is taken from 0. The measure at the end is 12. The combined length is 12 centimeters.

The count or measure of a quantity can be repeatedly added or multiplied.

The multiplication results in count or measure of the combined quantity.

What is the result of 3 repeatedly added 4 times? multiplication in number line is given in the figure.

• 34
• 34
• 3xx4=12

The answer is '12'. Multiplication 3xx4 is given in number-line. The value 3 is repeated 4 times to land in 12. The result of the multiplication is 12.

Which of the following is a meaning for the word "multiplication"?

• increase in quantity many times over
• increase in quantity many times over
• many possibilities or choices

The answer is "increase in quantity many times over".

What is the term used to refer "increase in quantity many times over"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "multiplication".

Multiplication - First Principles : Two numbers are considered, each of which represents a count or measurement. One of the amount is repeated the number of times given by the second amount to form the result representing the collective amount from such repetition.

eg: 12 xx 3 = 36

12 is the multiplicand

3 is the multiplier

36 is the product

Which of the following is a meaning for the word "multiplicand"?

• process of multiplication which is repeated addition
• the number or quantity that is repeatedly added in a multiplication
• the number or quantity that is repeatedly added in a multiplication

The answer is "the number or quantity that is repeatedly added in a multiplication".

What is the term used to refer "the number that is repeatedly added"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "multiplicand".

Which of the following is a meaning for the word "multiplier"?

• the number of times a quantity is repeatedly added
• the number of times a quantity is repeatedly added
• a tool that helps to hold an object firmly

The answer is "the number of times a quantity is repeatedly added".

What is the term used to refer "the number of times a quantity is repeatedly added"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "multiplier".

Which of the following is a meaning for the word "product"?

• the result of multiplication
• the result of multiplication
• professionally made passageway for air

The answer is "the result of multiplication".

What is the term used to refer "the result of multiplication"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "product".

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