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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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mathsIntegersInteger Multiplication & Division

Integer Multiplication: Simplified Procedure

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



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In whole numbers, we had studied the following.

Multiplication by Place-value with Regrouping - Simplified Procedure : Two numbers are multiplied as illustrated in the figure.multiplication Note: The procedure combines `10` units into `1` ten as carry over and so on for higher place-values.

What is the product of `4` and `3`?

By first principles, `text(received:)4` is repeatedly put in `3` times.

  • `43`
  • `12`
  • `12`

The answer is "`12`"

What is the product of `-4` and `3`?

By first principles, `text(given:)4` is repeatedly put in `3` times.

  • `-12`
  • `-12`
  • `+12`

The answer is "`-12`"

What is the product of `4` and `-3`?

By first principles, `text(received:)4` is repeatedly taken away `3` times.

  • `-12`
  • `-12`
  • `+12`

The answer is "`-12`"

What is the product of `-4` and `-3`?

By first principles, `text(given:)4` is repeatedly taken away `3` times.

  • `-12`
  • `+12`
  • `+12`

The answer is "`+12`"

Summary of integer multiplication illustrative examples:

 •  `4xx3 = 12`
`text(received:)4` is put-in `3` times

 •  `(-4)xx3 = -12`
`text(given:)4` is put-in `3` times

 •  `4xx(-3) = -12`
`text(received:)4` is taken-away `3` times

 •  `(-4)xx(-3) = 12`
`text(given:)4` is taken-away `3` times

Based on this, the multiplication is simplified as

 •  +ve `xx` +ve `=` +ve

 •  -ve `xx` +ve `=` -ve

 •  +ve `xx` -ve `=` -ve

 •  -ve `xx` -ve `=` +ve

Integer Multiplication -- Simplified Procedure : The sign of the product is decided by signs of multiplicand and multiplier as follows.

Sign-Property of Integer Multiplication
 •  positive `xx` positive `=` positive
 •  positive `xx` negative `=` negative
 •  negative `xx` positive `=` negative
 •  negative `xx` negative `=` positive

The absolute value of the product is calculated by whole number multiplication of absolute values of the multiplicand and multiplier.

Solved Exercise Problem:

Find the product of the multiplication `22 xx (-1)`

  • `-11`
  • `-22`
  • `-22`

The answer is "`-22`"

Solved Exercise Problem:

Find the product of the multiplication `0xx(-32)`

  • `0`
  • `-0`
  • both the above
  • both the above

The answer is "both the above"

Solved Exercise Problem:

Find the product of the multiplication `-222 xx (-88)`

  • `-19536`
  • `19536`
  • `19536`

The answer is "a positive number".

                            
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