SS1: MATHEMATICS  1ST TERM

Number Base System I  Week 16 Topics2 Quizzes

Number Base System II  Week 23 Topics

Number Base System III  Week 32 Topics1 Quiz

Modular Arithmetic I  Week 42 Topics

Modular Arithmetic II  Week 52 Topics

Modular Arithmetic III  Week 63 Topics1 Quiz

Indices I  Week 73 Topics

Indices II  Week 81 Topic1 Quiz

Logarithms I  Week 93 Topics

Logarithms II  Week 104 Topics1 Quiz
Participants 9899

Do you like this content?
Follow us
The Cyclic Event
A good example of cyclic event is the 12hour clock. In the 12hour clock arithmetic, the hour hand can move in both directions as shown the diagram
Example 1
If the time is presently 9 oâ€™clock, what would the time be in:
(i) 92 hours
(ii) 750 hoursâ€™ time?
Solution
(i) 92 hours = 92 Ã· 12 = 7 r 8
= ( 12 x 7) hrs + 8 hrs
= 9 oâ€™clock + 8hrs
= 5 oâ€™clock
(ii) 750 hours = 750 Ã· 12 = 62 r 6
= (12 x 62)hrs + 6 hrs
= 9 oâ€™clock + 6 hrs
= 3 oâ€™clock
Example 2
If the time is presently 3 oâ€™clock, what time was it
(i) 9 hours ago
(ii) 25 hours ago?
Solution:
(i) Counting in the anticlockwise direction, i.e. we have to count 9 spaces backwards i.e. the time was 6 oâ€™clock.
(ii) 25 = (12 x 2)hrs + 1 hr
Hence, counting one step backwards (or in an anticlockwise direction), we have (3 â€“ 1) = 2
i.e. 2 oâ€™clock
The clock arithmetic is synonymous with Modular Arithmetic which is by way of wrapping numbers around after they reach a certain value.
Modular Arithmetic system involves integers only. When an integer is divided by 5, the possible remainders are 0, 1, 2, 3, and 4; we thus refer to these numbers as the residues of modulo 5 or mod5.
Similarly, 0, 1, 2, consist of the set of residues for mod 3.
0, 1, 2, 3, consist of the set of residues for mod 4.
0, 1, 2, 3, 4, 5 consist of the set of residues for mod 6.
In general, {0, 1, 2, 3, 4, 5, 6, …… n – 1} is called the set of residues for mod n.
Responses