CONTENT
- Concept of Modular Arithmetic
- Addition, Subtraction and Multiplication Operations in Module Arithmetic
- Application to daily life.
Modular Arithmetic
In the previous section, we discovered a new kind of arithmetic, where we add positive integers by roating in number cycle. This arithmetic is called modular arithmetic. In our example, we ignored multiples of 4 and concentrated on the remainders. In this case we say that the modulus is 4
For example,
5 = 1 (mod 4)
Where mod 4 means with modulus 4 or modulo 4.
Note that 9÷ 4 = 2, remainder 1
And 45 ÷ 4 = 11 remainder 1
We say that 9 and 45 are equal modulo 4,
i.e. 9 = 45 = 1 (mod 4)
Example 1
Reduce 55 to its simplest form:
Modulo 3
Modulo 4
Modulo 5
Modulo 6
55 ÷ 3 = 18, remainder 1
55 = 1 (mod 3)
55 ÷ 4 = 13, remainder 3
55 = 3 (mod 4)
55 ÷ 5 = 11, remainder 0
55 = 0 (mod 5)
55 ÷ 6 = 9, remainder 1
55 = 1 (mod 6)
EVALUATION
Write down the names of four markets in your locality which are held in rotation over 4* days.
Addition, Subtraction and Multiplication Operations in Module Arithmetic
Addition and Subtraction
The table below shows an addition table (mod 4) in which numbers 0, 1, 2 and 3 are added to themselves.
READING ASSIGNMENT
New General Mathematics for SS 1 Page 239 ex. 20c 1 – 10
WEEKEND ASSIGNMENT
Find the simplest form of the following in the given moduli.
- -75 (mod 7)A. 4 B. 2 C. 5 D. 7
- -56 (mod 13)A. 10 B. 5 C. 9 D. 12
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