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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.
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Fractions as Directed Numbers

Fractions are also directed numbers. That is, Fractions with positive and negative values are explained.

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Whole numbers representation is not sufficient to represent directed numbers.

For example, consider the numbers in
• I received 3 candies and
& bull; I gave 3 candies.

In the whole numbers, both these are represented as 3.

In integers, the first is +3 and the second is -3.

Integer numbers are represented as follows.

3 is represented as either text(received:)3 or text(aligned:)3.

-3 is represented as either text(given:)3 or text(opposed:)3.

The English word "integer" means "untouched", that is, the numbers are not cut into smaller pieces or fractions.

Are fractions directed numbers?

Consider the problem. A girl receives 2/3 candy from her brother. Later, she gives 1/3 candy back.

These fractions have an additional property

•  2/3 : amount received

•  1/3 : amount given

In this problem, received and given represent two directions.

Fractions are Directed Numbers : Fractions are represented as directed numbers with positive and negative signs.

eg: 2/5 represents text(received:)2/5 or text(aligned:)2/5. This fraction represents 2 counts of amount with 1/5 place value.

-2/5 represents text(given:)2/5 or text(opposed:)2/5. This fraction represents -2 counts of amount with 1/5 place value.

The word "directed" means aimed in a particular direction.

Absolute value of a directed number is given as the count or measure without the direction information.

The sign of a directed number is the direction information of the number.

The operator | | represents the absolute value of the number.

Solved Exercise Problem:

What is the absolute value of -1/3?

• 1/3
• 1/3
• 0

The answer is "1/3"

Solved Exercise Problem:

What is the absolute value of 1/4?

• same value 1/4
• same value 1/4
• -1/4

The answer is "1/4"

Solved Exercise Problem:

What is |-1/2|?

• positive number 1/2
• positive number 1/2
• -1/2

The answer is "1/2"

Solved Exercise Problem:

What is the sign of -1/7

• 1/7
• negative
• negative

Solved Exercise Problem:

What is |2/7|?

• positive fraction 2/7
• positive fraction 2/7
• -27

The answer is "2/7"

Solved Exercise Problem:

What is the sign of 2/7?

• positive
• positive
• negative

Solved Exercise Problem:

What is |-3/7|?

• positive fraction 3/7
• positive fraction 3/7
• -3/7

The answer is "3/7"

Solved Exercise Problem:

What is the sign of -3/7 ?

• positive
• negative
• negative