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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.
mathsIntegersIntroduction to Integers (directed whole numbers)

### Handling Direction in Integers

This page explains handing positive and negative numbers, specifically the meaning of negative of a positive number, and negative of a negative number.

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To explain the concepts the following mapping is used.

text(received:)3 = +3 = 3
text(given:)3 = -3

This models the directed numbers of various forms.
eg: temperature 3^@ above and below 0^@ is modeled as text(received:)3 =3 and text(given:)3 =-3.

The explanation in this is going to be little involved. Students can spend a little extra time thinking about the given questions and answer.

Which of the following is text(received:)3?

• +3
• +3
• -3

The answer is "+3"

Which of the following is text(given:)3?

• +3
• -3
• -3

The answer is "-3"

Is text(received:)(-3) a number?

• no such number is possible
• no such number is possible
• knowing that -3 is text(given:)3 ; it is text(received:)(text(given:)3)

The answer is "text(received:)(text(given:)3)".

Is text(given:)(-3) a number?

• no such number is possible
• no such number is possible
• knowing that -3 is text(given:)3 ; it is text(given:)(text(given:)3)

The answer is "text(given:)(text(given:)3)".

To understand the two numbers text(received:)(-3) and text(given:)(-3), let us consider an example application.

A girl has a box of candies. The number of candies in the box is not counted. But she maintains a daily account of how many are received or given.

She received 3 candies yesterday. How many candies were received yesterday?

• text(received:)3 = +3
• text(received:)3 = +3
• text(given:)3 = -3

The answer is "text(received:)3 = +3".

Considering the box of candies and the daily account of number of candies received or given.

She gave 3 candies today. How many candies are received today?

• text(received:)3 = +3
• text(given:)3 = -3
• text(given:)3 = -3

The answer is "text(given:)3 = -3".

Considering the box of candies and the daily account of number of candies received or given.

Her brother took 3 candies and so, she noted received or put-in -3 candies today. What does this number text(received:)(-3) mean?

• text(received:)(-3) = text(given:)3 = -3
• text(received:)(-3) = text(given:)3 = -3
• text(received:)(-3) = +3

The answer is "text(received:)(-3) = text(given:)3 = -3".

Considering the box of candies and the daily account of number of candies received or given.

Her brother returned 3 candies which was given earlier and so, she noted given or taken away -3 of an earlier date. What does this number text(given:)(-3) mean?

• text(given:)(-3) = text(given:)3 = -3
• text(given:)(-3) = text(received:)3 = +3
• text(given:)(-3) = text(received:)3 = +3

The answer is "text(given:)(-3) = text(received:)3 = +3".

Handling Sign in Integers :
received 3
text(received:)3 = 3

given 3
text(given:)3 = -3

received -3 is put-in given 3
text(received:)(-3) = +(-3) = -3

given -3 is taken-away given 3
text(given:)(-3) = -(-3) = 3

Solved Exercise Problem:

What is -(+7)?

• +7
• -7
• -7

The answer is '-7'.

Solved Exercise Problem:

What is -(-7)?

• +7
• +7
• -7

The answer is '7'.

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