SS1 Second Term Mathematics Lesson Note – Modular Arithmetic II

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CLASS: SS 1

TOPIC: Modular Arithmetic

CONTENT:

• Addition, Subtraction, Multiplication and Division operations in module arithmetic
• Application to daily life

ADDITION AND SUBTRACTION:

In modular arithmetic, addition and subtraction are symbolized by ⊕ and ⊖ respectively.  In the table we enter only the remainders when a pair of elements in the ⊕ on the set {0,1,2,3,4} modulo 5

⊕	0	1	2	3	4
0	0	1	2	3	4
1	1	2	3	4	0
2	2	3	4	0	1
3	3	4	0	1	2
4	4	0	1	2	3

Addition ⊕ in mod 5

1. Simplify  Find 39  ⊕  29(mod 6)

Solution:   39  ⊕   29= 68

= (6×11+2)

= 2(mod 6)

2. Calculate the following in the given moduli   (a) 12Θ5(mod 4)   (b) 38 Θ42(mod 7)

Solution:  (a)  12Θ5 = 7

7 = 4 + 3

= 3(mod 4)

(b)   38 Θ 42 = 4

4 = 7 + 3

= 3(mod 7)

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