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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.

click on the content to continue..

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".

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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