Properties of Modular Arithmetic Quiz

What is the commutative property of addition in modular arithmetic?

• The order of the numbers being added does not affect the result.

• The order of the numbers being added affects the result

• The result of the addition is always negative

• The result of the addition is always zero

State the associative property of addition in modular arithmetic.

• The result of (a + b) modulo n is congruent to the result of (a modulo n) + (b modulo n)

• The result of (a + b) modulo n is congruent to the result of (a modulo n) - (b modulo n)

• The result of (a + b) modulo n is congruent to the result of (a modulo n) * (b modulo n)

• For any three integers a, b, and c, (a + b) + c is congruent to a + (b + c) modulo n.

Explain the associative property of multiplication in modular arithmetic.

• For any three integers a, b, and c, (a * b) mod c is equal to (a mod c * b mod c) mod c

• The associative property of multiplication in modular arithmetic is (a * b) mod c = (a + b) mod c

• The associative property of multiplication in modular arithmetic is (a * b) mod c = (a mod c) * (b mod c)

• The associative property of multiplication in modular arithmetic is (a * b) mod c = (b * a) mod c

Define the distributive property in modular arithmetic.

• ((a mod n) * (b mod n)) mod n

• ((a mod n) - (b mod n)) mod n

• ((a mod n) + (b mod n)) mod n

• ((a + b) mod n) + ((a - b) mod n)

Find the congruence class of 7 modulo 3.

• 2

• 4

• 6

• 1

Find the congruence class of 12 modulo 5.

• 7

• 3

• 5

• 2

What is the result of (a + b) mod n, where a ≡ c (mod n) and b ≡ d (mod n)?

• (c - d) mod n

• (a + b) mod n

• (c + d) mod n

• (a - b) mod n

If a ≡ b (mod n), what can be said about a + c ≡ b + c (mod n)?

• a + c ≡ b * c (mod n)

• a + c ≡ b + c (mod n)

• a + c ≡ b - c (mod n)

• a + c ≡ b / c (mod n)

If a ≡ b (mod n), what can be said about a * c ≡ b * c (mod n)?

• a - c ≡ b - c (mod n)

• a + c ≡ b + c (mod n)

• a * c ≡ b * c (mod n)

• a / c ≡ b / c (mod n)

Explain the concept of modular arithmetic and its applications in real life.

• Modular arithmetic is a system of arithmetic for fractions, where numbers are rounded up to the nearest whole number.

• Modular arithmetic is a system of arithmetic for decimals, where numbers are rounded to the nearest tenth.

• Modular arithmetic is a system of arithmetic for integers, where numbers wrap around after reaching a certain value. It has applications in cryptography, computer science, and music theory.

• Modular arithmetic is a system of arithmetic for negative numbers, where numbers are multiplied by -1.