(a) Copy and complete the following table for multiplication modulo 11.
1
5
9
10
1
1
5
9
10
5
5
9
9
10
10
Use the table to : (i) evaluate ; (ii) find the truth set of :(1) ; (2) (b) When a fraction is reduced to its lowest term, it is equal to . The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.
Explanation
(a)
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) (ii) (1) By comparison, . (2) From the table, Hence, n = 9. (b) Let the fraction = Put (2) in (3), Hence, the fraction = .