The set of positive rational numbers forms a group under the operation a * b = ab/10. Find the identity element.

The set of positive rational numbers forms a group under the operation $a * b = \frac{ab}{10}$ . Find the identity element.

Model answer

Also accepted: e=10, e = 10

Explanation

The identity

e

satisfies

a*e=a

for every

a

, so

\dfrac{ae}{10}=a

. Dividing by

a

, which is never zero here, gives

\dfrac{e}{10}=1

and so

e=10

. Note that 10 is itself a positive rational, so it belongs to the set.

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

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