If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?

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Question: If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?

Options:

Correct Answer: 1

Solution:

a + b ≡ 3 + 5 ≡ 8 ≡ 1 (mod 7).

If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?

If a ≡ 3 (mod 7) and b ≡ 5 (mod 7), what is a + b (mod 7)?

Step 1: Understand the notation 'a ≡ 3 (mod 7)'. This means when you divide 'a' by 7, the remainder is 3.
Step 2: Understand the notation 'b ≡ 5 (mod 7)'. This means when you divide 'b' by 7, the remainder is 5.
Step 3: Add the two values: 3 (from a) + 5 (from b) = 8.
Step 4: Now, we need to find 8 (mod 7). This means we divide 8 by 7 and find the remainder.
Step 5: When we divide 8 by 7, the quotient is 1 and the remainder is 1 (because 8 - 7 = 1).
Step 6: Therefore, 8 (mod 7) is equal to 1.
Step 7: So, a + b (mod 7) is equal to 1.

Modular Arithmetic – Understanding how to perform addition and reduction of numbers under a modulus.