If a number is divided by 12 and gives a remainder of 7, what will be the remain

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Question: If a number is divided by 12 and gives a remainder of 7, what will be the remainder when this number is divided by 3?

Options:

Correct Answer: 1

Solution:

Since 7 divided by 3 gives a remainder of 1, the answer is 1.

If a number is divided by 12 and gives a remainder of 7, what will be the remainder when this number is divided by 3?

If a number is divided by 12 and gives a remainder of 7, what will be the remainder when this number is divided by 3?

Step 1: Understand that when a number is divided by 12 and gives a remainder of 7, it can be written 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: First, divide 12 by 3. The result is 4 with a remainder of 0. This means 12k will not affect the remainder when divided by 3.
Step 4: Now, focus on the remainder of 7 when divided by 3.
Step 5: Divide 7 by 3. The result is 2 with a remainder of 1.
Step 6: Therefore, the remainder when the original number is divided by 3 is 1.

Modular Arithmetic – Understanding how remainders work when dividing numbers.
Properties of Remainders – Using the properties of remainders to simplify calculations.