In a clock arithmetic system, if it is currently 9 o'clock, what time will it be

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Question: In a clock arithmetic system, if it is currently 9 o\'clock, what time will it be in 15 hours?

Options:

Correct Answer: 1 o\'clock

Solution:

In modular arithmetic with a modulus of 12 (for hours), 9 + 15 = 24, and 24 mod 12 = 0, which corresponds to 12 o\'clock.

In a clock arithmetic system, if it is currently 9 o'clock, what time will it be in 15 hours?

In a clock arithmetic system, if it is currently 9 o'clock, what time will it be in 15 hours?

Step 1: Start with the current time, which is 9 o'clock.
Step 2: Add the number of hours you want to move forward, which is 15 hours.
Step 3: Calculate the total time by adding 9 and 15. This gives you 24.
Step 4: Since we are using a 12-hour clock, we need to find the equivalent time in a 12-hour format. This is done using modular arithmetic.
Step 5: To find the equivalent time, calculate 24 mod 12. This means you divide 24 by 12 and find the remainder.
Step 6: 24 divided by 12 equals 2 with a remainder of 0. So, 24 mod 12 = 0.
Step 7: In a 12-hour clock system, 0 corresponds to 12 o'clock.

Modular Arithmetic – Understanding how to perform addition and find remainders within a fixed range, specifically using a modulus of 12 for hours on a clock.
Time Calculation – Calculating future times based on a starting point and a given duration, while considering the cyclical nature of a clock.