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Thought-Process to Discover Knowledge

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mathsFractionsArithmetics with Fractions

### Reciprocal of a fraction

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The word "reciprocal" means: 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.

familiarize with the terminology
reciprocal

"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 3/4has to be converted to equivalent improper fraction 7/4 before finding the reciprocal 4/7

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