Patterns and Properties in Modular Multiplication

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1) If a ≡ 2 (mod 5), what is a × 3 (mod 5)?

Explanation

2 × 3 = 6; 6 mod 5 = 1.

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About This Quiz
Patterns And Properties In Modular Multiplication - Quiz

Numbers in modular arithmetic follow special patterns! In this quiz, you’ll explore the rules and shortcuts of modular multiplication, including how congruences interact and why the “mod” step makes math cleaner. We bring you this quiz so you can see beyond the calculations and notice the underlying properties.

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2) If a ≡ 4 (mod 6), what is 2a (mod 6)?

Explanation

2 × 4 = 8; 8 mod 6 = 2.

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3) Which pair is not congruent (mod 7)?

Explanation

7×3 = 21 ≡ 0 (mod 7), 5×5 = 25 ≡ 4 (mod 7). Not equal, so not congruent.

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4) Compute (7 × 11) mod 9.

Explanation

7 × 11 = 77; 77 mod 9 = 5.

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5) If 8 × x ≡ 4 (mod 12), what is one solution for x?

Explanation

8 × 2 = 16; 16 mod 12 = 4.

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6) If a ≡ 3 (mod 4), what is a² (mod 4)?

Explanation

3² = 9; 9 mod 4 = 1.

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7) Compute (15 × 18) mod 7.

Explanation

15 × 18 = 270; 270 mod 7 = 4.

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8) Which of the following is true?

Explanation

Option b accurately represents a fundamental property of modular arithmetic known as the distributive property. This property states that the product of two numbers, taken modulo n, is equivalent to first taking each number modulo n, multiplying them, and then taking that product modulo n. The other options are incorrect as they either misrepresent the nature of modular multiplication or state false properties about it.

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9) If a ≡ 2 (mod 9) and b ≡ 5 (mod 9), what is ab mod 9?

Explanation

ab = 2 × 5 = 10. Divide 10 by 9 → remainder 1.

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10) Compute (23 m 17) mod 10.

Explanation

23 × 17 = 391; 391 mod 10 = 1.

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If a ≡ 2 (mod 5), what is a × 3 (mod 5)?
If a ≡ 4 (mod 6), what is 2a (mod 6)?
Which pair is not congruent (mod 7)?
Compute (7 × 11) mod 9.
If 8 × x ≡ 4 (mod 12), what is one solution for x?
If a ≡ 3 (mod 4), what is a² (mod 4)?
Compute (15 × 18) mod 7.
Which of the following is true?
If a ≡ 2 (mod 9) and b ≡ 5 (mod 9), what is ab mod 9?
Compute (23 m 17) mod 10.
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