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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3Topics
    |
    1 Quiz
  3. Number Base System III | Week 3
    2Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2Topics
  5. Modular Arithmetic II | Week 5
    2Topics
  6. Modular Arithmetic III | Week 6
    3Topics
    |
    1 Quiz
  7. Indices I | Week 7
    2Topics
  8. Indices II | Week 8
    1Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3Topics
  10. Logarithms II
    1Topic
    |
    1 Quiz
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Multiplication in Modular Arithmetic

Multiplication can be explained as repeated addition e.g. 4 ⊗ 3 (mod 5) i.e.

\( \scriptsize 3 \: + \: 3 \: + \: 3 \: + \: 3 = 12  \\ \scriptsize = 2(mod 5) \)

i.e.  \(\scriptsize 4 \: \bigotimes \: 3 = 2 (mod\:5) \)

The table below shows multiplication in modulo 5.

\(\scriptsize \bigotimes \)01234
000000
101234
202341
303142
404321

For example, 3 ⊗ 2 means 3 on the residues column against 2 on the residues row, the result is 1.

i.e.    3 ⊗ 2 (mod 5) = 1 (mod 5)

\(\scriptsize \bigotimes \)01234
000000
101234
202341
303142
404321

Division

As a matter of fact, division is the inverse of multiplication, thus we can use multiplication table to solve division problems.

For example, 3 ⨸ 4 = ? (mod 5)

Let 3 ⨸ 4 = a

Then 4a = 3  \(\scriptsize since \left (\; \normalsize \frac{3}{4} = \scriptsize a, \; then \; 4a = 3 \right) \)

It implies that a number (a) multiplied by 4 in mod 5 equals 3. From the table check for 4 on the residues column and 3 on the residues row

\( \scriptsize \therefore a = 2 \)

i.e. 3 ⨸ 4 = 2 (mod 5)

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