Clock Arithmetic Quiz: Clock Arithmetic with Remainders

  • 5th Grade
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Quizzes Created: 7682 | Total Attempts: 9,547,133
| Questions: 20 | Updated: Dec 17, 2025
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1) On a 12-hour clock, what time is 9 + 5 hours?

Explanation

Compute (9 + 5) mod 12 = 14 mod 12 = 2. So the clock shows 2.

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About This Quiz
Clock Arithmetic Quiz: Clock Arithmetic With Remainders - Quiz

Why does arithmetic behave differently when working with remainders, like the hours on a clock? In this quiz, you’ll explore modular arithmetic by examining how numbers “wrap around” after reaching a certain limit. You’ll practice adding and subtracting within a modulus, interpreting remainder-based results, and connecting each idea to real... see moretimekeeping. Through guided examples, you’ll gain intuition for modular reasoning and understand how it applies to patterns, cycles, and problem-solving situations.
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2) On a 12-hour clock, 15 ≡ 3 (mod 12).

Explanation

15 − 3 = 12, which is a multiple of 12. So 15 ≡ 3 (mod 12).

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3) On a 12-hour clock, 7 + 19 hours = ____.

Explanation

7 + 19 = 26; 26 mod 12 = 2.

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4) On a 24-hour clock, 22:00 + 7 hours = ____

Explanation

Compute (22 + 7) mod 24 = 29 mod 24 = 5. So it reads 05:00.

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5) Select all numbers congruent to 4 (mod 12).

Explanation

Reduce mod 12: 16→4, 28→4, 40→4, −8 ≡ 4 (since −8 + 12 = 4), while 3 ≡ 3.

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6) On a 24-hour clock, 24 ≡ 0 (mod 24).

Explanation

24 − 0 = 24, a multiple of 24. So 24 ≡ 0 (mod 24).

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7) On a 12-hour clock, 11 + 15 hours = ____.

Explanation

11 + 15 = 26; 26 mod 12 = 2.

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8) On a 12-hour clock, starting at 3 and adding 50 hours gives ____

Explanation

(3 + 50) mod 12 = 53 mod 12. Since 12×4 = 48, remainder 5.

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9) On a 24-hour clock, which totals are congruent to 18 (mod 24)?

Explanation

Each equals 18 + 24k: 42=18+24, 66=18+48, 90=18+72, 114=18+96.

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10) On a 12-hour clock, adding 12 hours leaves the same time.

Explanation

12 ≡ 0 (mod 12), so adding 12 hours does not change the display.

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11) On a 24-hour clock starting at 00:00, after 73 hours the clock reads ____.

Explanation

73 mod 24 = 1, so it reads 01:00.

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12) Which congruence is correct modulo 12?

Explanation

−5 mod 12 = 7 because −5 + 12 = 7. So 7 ≡ −5 (mod 12). The others are not true modulo 12.

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13) Select all pairs (a,b) with a ≡ b (mod 12).

Explanation

Compute remainders mod 12: 25→1, 1→1; 14→2, 2→2; 18→6 vs 7 (not equal); −1→11, 11→11; 5→5, 17→5.

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14) On a 12-hour clock, 8 + 20 hours equals 4.

Explanation

(8 + 20) mod 12 = 28 mod 12 = 4.

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15) On a 24-hour clock, 5 − 13 hours = ____.

Explanation

5 − 13 = −8; −8 mod 24 = 24 − 8 = 16.

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16) On a 12-hour clock, 10 + 35 hours = ____

Explanation

(10 + 35) mod 12 = 45 mod 12. Since 12×3=36, remainder 9.

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17) Modulo 24, which numbers are congruent to −1?

Explanation

Compute mod 24: 23 ≡ −1; −25 ≡ −1 (add 24 to get −1); 47 = 24×1 + 23 ≡ −1; 1 ≡ 1; 71 = 24×2 + 23 ≡ −1.

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18) On a 12-hour clock, 13:00 shows as 1:00.

Explanation

13 ≡ 1 (mod 12), so 13:00 is displayed as 1:00.

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19) On a 12-hour clock starting at 12, after 115 hours it will read ____.

Explanation

Treat 12 as 0: 115 mod 12 = 7, so the display is 7.

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20) On a 24-hour clock, 06:00 − 19 hours = ____

Explanation

6 − 19 = −13; −13 mod 24 = 24 − 13 = 11. So the clock reads 11:00.

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On a 12-hour clock, what time is 9 + 5 hours?
On a 12-hour clock, 15 ≡ 3 (mod 12).
On a 12-hour clock, 7 + 19 hours = ____.
On a 24-hour clock, 22:00 + 7 hours = ____
Select all numbers congruent to 4 (mod 12).
On a 24-hour clock, 24 ≡ 0 (mod 24).
On a 12-hour clock, 11 + 15 hours = ____.
On a 12-hour clock, starting at 3 and adding 50 hours gives ____
On a 24-hour clock, which totals are congruent to 18 (mod 24)?
On a 12-hour clock, adding 12 hours leaves the same time.
On a 24-hour clock starting at 00:00, after 73 hours the clock reads...
Which congruence is correct modulo 12?
Select all pairs (a,b) with a ≡ b (mod 12).
On a 12-hour clock, 8 + 20 hours equals 4.
On a 24-hour clock, 5 − 13 hours = ____.
On a 12-hour clock, 10 + 35 hours = ____
Modulo 24, which numbers are congruent to −1?
On a 12-hour clock, 13:00 shows as 1:00.
On a 12-hour clock starting at 12, after 115 hours it will read ____.
On a 24-hour clock, 06:00 − 19 hours = ____
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