(a)

\(\otimes\)	1	5	9	10
1	1	5	9	10
5	5	3	1	6
9	9	1	4	2
10	10	6	2	1

(i) \((9 \otimes 5) \otimes (10 \otimes 10) = 1 \otimes 1 = 1\)
(ii) (1) \(10 \otimes m = 2\)
By comparison, \(10 \otimes 9 = 2\).
(2) \(n \otimes n = 4\)
From the table, \(9 \otimes 9 = 4\)
Hence, n = 9.
(b) Let the fraction = \(\frac{m}{n}\)
\(\frac{m}{n} = \frac{3}{4}..... (1)\)
\(\implies n = \frac{4m}{3} ....... (2)\)
\(2m = n + 34 ...... (3)\)
Put (2) in (3),
\(2m = \frac{4m}{3} + 34\)
\(2m - \frac{4m}{3} = 34 \implies \frac{2m}{3} = 34\)
\(m = \frac{34 \times 3}{2} = 51\)
\(n = \frac{4m}{3} = \frac{4 \times 51}{3} = 68\)
Hence, the fraction = \(\frac{51}{68}\).