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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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mathsCommercial ArithmeticsComparing Quantities

### Comparing Quantities

In numerical arithmetics comparing two numbers is done by specifying one number as greater than, equal-to, or smaller than the other. To have a better comparison, the relative magnitude of the numbers are specified using numbers.

Numbers represent quantities. eg: length of a rope is 2m.

Numbers are also used to Compare quantities: eg: Length of a rope is 2 times of length of the pole.

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The distance to a town P is 120 km and to another town Q is 240 km. Which one is farther?

• Town P is farther
• Town Q is farther
• Town Q is farther

The answer is "Town Q is farther".

The distance to a town P is 120 km and to another town Q is 240 km.

Town Q is calculated to be farther by comparing the numbers 120 and 240.

In comparing two numbers p and q, only one of the following is true.

•  p equals q

•  p is greater than q

•  p is lesser than q

In this case, p=120 is lesser than q=240.

This is called trichotomy property of numbers.

Comparing two numbers p=120 and q=240, it is given than q is greater.

Consider the numbers r=1212 and s=120000. It is evident that all the numbers q, r, and s are greater than p.

Which of the following information is missing in this comparison?

• magnitude of the numbers, whether the numbers are almost equal, or far greater
• magnitude of the numbers, whether the numbers are almost equal, or far greater
• no information is missing

The answer is "magnitude of the numbers, whether the numbers are almost equal, or far greater".

Comparing two numbers p=120 and q=240

Apart from saying q is greater, which of the following comparison helps to understand the numbers better?

• q is double of p
• q is double of p
• q is greater than p

The answer is "q is double of p". If p is multiplied by 2, we get q.
120 xx 2 = 240

Comparing numbers p=120 with q=240, r=122 and s=120000.

q is 2 times p

r is 1.1 times p (You will learn about decimal 1.1 in some time.)

s is 1000 times p.

Now the relative magnitudes of q, r, s are easily understood.

There are formal ways to specify the comparison. Those are ratios, proportions, and percentage.

Numbers represent quantities.

•  The number of pens in the box is 2

•  Length of a rope is 1 1/2 meters

•  1/4th of the apple is remaining

Numbers are also used to compare quantities.

•  The number of pens in the red box is 2 times the number of pens in the blue box

•  Length of rope is 1 1/2 times the height of the table.

•  The number of apples he had is 1/4th of the number she had.

When a number is specified, a context is provided and the meaning of the number is defined in the context.

For example, Consider:

Length of a rope is 1 1/2 meter. The context in this specifies the measure of the quantity.
Length of the rope is 1 1/2 times the height of the table. The context in this specifies the comparison of one quantity to another.

While learning ratios, proportions, and percentage, the context becomes very important. The specifics of the context is explained in the due course of this lesson.

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