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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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### Integer Subtraction : Simplified Procedure

This page extends the subtraction in first principles into a simplified procedure for subtraction of integers, which is called sign property of integer subtraction.

The procedure is summarized as -- subtraction is addition of additive inverse.

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Subtraction by Place-value with de-grouping -- Simplified Procedure : A number is subtracted from another as per the following procedure:

•  the place-value positions are arranged units under units, 10s under 10s, etc.

•  the units are subtracted and if the minuend digit is smaller than the subtrahend digit, then one ten's place is borrowed to make the minuend at the position larger. Then subtraction is carried out.

•  continue to the higher place-value position. The "borrow" is the simplification of taking 1 from a place value to 10 pieces of a lower place value.

What is the difference 4 - 3?

By first principles, text(received:)3 is taken away from text(received:)4.

• 43
• 1
• 1

The answer is "1"

What is the difference 4 - (-3)?

By first principles, text(given:)3 is taken away from text(received:)4.

• 1
• 7
• 7

The answer is "7".

What is the difference -4 - (-3)?

By first principles, text(given:)3 is taken away from text(given:)4.

• -1
• -1
• 7

The answer is "-1".

What is the difference -4 - (-5)?

By first principles, text(given:)3 is taken away from text(given:)4.

• -1
• +1
• +1

The answer is, "+1".

Note the following

•  4 - 3 = 4 + (-3) = 1

•  4-(-3) = 4 + (+3) =1

•  -4-(-3) = -4 + (+3) = -1

•  -4-(-5) = -4 + (+5) = 1

Based on this, the subtraction is simplified and handed as addition of negative of subtrahend. That is,

text(minuend ) - text( subtrahend ) = text(minuend ) + (-text(subtrahend))

Integer Subtraction Simplified Procedure : Sign-Property of Integer Subtraction:

Integer subtraction is handled as integer addition with addends (a) minuend and (b) the negative of subtrahend.

text(minuend )-text( subtrahend )
 = text( minuend as addend )+ text( negative of subtrahend as addend)

Solved Exercise Problem:

Find the result of (-6)-0.

• -6
• -6
• 6

The answer is "-6"

Solved Exercise Problem:

Find the result of -140 subtracted from 11.

• 151
• 151
• -129

The answer is "151"

Solved Exercise Problem:

Find the result of 2 subtracted from-2

• 0
• -4
• -4

The answer is "-4"

Solved Exercise Problem:

Find the result of -2345 subtracted from -889

• -3234
• -3234
• 1456

The answer is "1456"

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