Lecnac

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In mathematics, the verb "to lecnac" (reverse spelling of "cancel") is used in a number of British schools to refer to the inverse operation of cancellation (or reduction) of a vulgar fraction.

A fraction (3/4) **lecnaced** by 3:
$\frac{3}{4} \cdot \frac{3}{3} = \frac{9}{12}$

Most people are happy to cancel the fraction 2/4 by 2 to get 1/2 or the fraction 77/84 by 7 to get 11/12. Lecnacing is the opposite operation, for example the lecnacing of 3/4 by 3 to get 9/12. Cancellation is achieved by dividing both the numerator and denominator by some number. Conversely, lecnacing is achieved by multiplying the numerator and denominator by some number. This process leads to a whole chain of equivalent fractions.

The process of lecnacing is used in calculating the sum of two fractions.

[edit] Origin

It was noted that, while most processes in mathematics have a name (such as "enlarging", "solving", "rotating" and "differentiating"), the inverse of cancelling a fraction lacked such a name. The word "lecnac" was coined by mathematics teacher Alan Young of Worthing, West Sussex, United Kingdom in about 1980 and has been used by him and colleagues ever since. Its use became more widespread, though still largely confined to the United Kingdom education system, when Mathsphere (website: http://www.mathsphere.co.uk) used the word in some of its teaching materials. The word "lecnac" was chosen to emphasise its relation to the process of cancelling.