If a number is divided by 12 and leaves a remainder of 7, what is the remainder

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Question: If a number is divided by 12 and leaves a remainder of 7, what is the remainder when the same number is divided by 3? (2023)

Options:

Correct Answer: 1

Exam Year: 2023

Solution:

Since 7 mod 3 = 1, the remainder when the number is divided by 3 is 1.

If a number is divided by 12 and leaves a remainder of 7, what is the remainder when the same number is divided by 3? (2023)

If a number is divided by 12 and leaves a remainder of 7, what is the remainder when the same number is divided by 3? (2023)

Step 1: Understand that when a number is divided by 12 and leaves a remainder of 7, it can be expressed as: number = 12k + 7, where k is some integer.
Step 2: We need to find the remainder when this number (12k + 7) is divided by 3.
Step 3: Break down the expression: 12k can be divided by 3 without a remainder because 12 is a multiple of 3.
Step 4: Now, focus on the remainder of 7 when divided by 3.
Step 5: Calculate 7 divided by 3. The quotient is 2 and the remainder is 1 (since 3 * 2 = 6 and 7 - 6 = 1).
Step 6: Therefore, the remainder when the number is divided by 3 is 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers, specifically how to find the remainder of a number when divided by different bases.