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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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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.

`text(received:)3 = text(aligned:)3 = + 3 = 3`

`text(given:)3 = text(opposed:)3 = -3`

Let us consider

`text(received:)(-3)`. We know that `-3` is `text(given:)3` and so the expression is simplified.

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

Let us consider

`text(given:)(-3)`. We know that `-3` is `text(given:)3` and so the expression is simplified.

`text(given:)(-3) ``= text(given:)(text(given:)3) ``= text(received:)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 gave `3` candies today. The number of candies received today is `-3`.

Her brother took `3` candies and so, she noted received or put-in `-3` candies today. This is represented as`text(received:)(-3) = -3`

Her brother returned `3` candies which was given earlier and so, she noted given or taken away negative `3` of an earlier date. Effectively this 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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