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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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mathsFractionsArithmetics with Fractions

Reciprocal of a fraction

In this page, reciprocal of a fraction is introduced.



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What does the word 'reciprocal' mean?

  • reuse; reprocess
  • reuse; reprocess
  • backwards; in reverse

The answer is 'backwards; in reverse'.

Consider the multiplication `4 xx 3`

 •  `4` is the multiplicand

 •  `3` is the multiplier

 •  `12` is the product

The multiplier has modified the multiplicand.
How to reverse or take backward the multiplication?
The reverse of the multiplier `3` is the reciprocal `1/3`
Because the product `12`, when multiplied by the reciprocal `1/3` gives the multiplicand `4`.

Reciprocal is also called the multiplicative inverse.

Consider the multiplication `2/3 xx 5/8=5/12`

 •  `2/3` is the multiplicand

 •  `5/8` is the multiplier

 •  `5/12` is the product

The reverse of the multiplier `5/8` is the reciprocal `8/5`
Because the product `5/12`, when multiplied by the reciprocal `8/5` gives the multiplicand `2/3`.

Reciprocal is also called the multiplicative inverse.

What is the fraction `2/3` to `3/2` called?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is 'reciprocal'. It is also called "multiplicative inverse"

"Reciprocal" or "multiplicative inverse" of a fraction is the fraction that inverses the number to a product result 1.

Reciprocal of a Fraction: For a fraction `p/q`, the "Reciprocal" or "multiplicative inverse" is `q/p` as `p/q xx q/p = 1`.

Solved Exercise Problem:

What is the reciprocal of `14/18 `?

  • `41/81`
  • `18/14`

The answer is '`18/14`'

Solved Exercise Problem:

What is the reciprocal of `1 3/4 `

  • `1 4/3`
  • `4/7`
  • `4/7`

The answer is '`4/7`'. The mixed fraction `1 3/4`has to be converted to equivalent improper fraction `7/4` before finding the reciprocal `4/7`

                            
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