Under the operation $a * b = \frac{ab}{10}$ on the positive rational numbers, write the inverse of an element $a$ in terms of $a$ .

Model answer

100/a

Also accepted: 100 / a, a^-1=100/a

Explanation

The identity for this operation is 10, so the inverse

a^{-1}

satisfies

a*a^{-1}=\dfrac{a\,a^{-1}}{10}=10

. Hence

a\,a^{-1}=100

and

a^{-1}=\dfrac{100}{a}

, which is a positive rational whenever

a

is.

Derived from ZIMSEC Further Mathematics 9187/1, November 2010, Q4

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