Modulo Remainders Quiz: Understanding Modular Math

  • 8th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) If two numbers have the same remainder when divided by n, they are congruent modulo n.

Explanation

That’s the definition of modular congruence.

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About This Quiz
Modulo Remainders Quiz: Understanding Modular Math - Quiz

Ever wonder why numbers loop back in such neat, predictable ways? This quiz takes you into the world of remainders, where every division leaves behind a clue. You’ll explore how modulo creates repeating patterns, uncover what those leftovers really mean, and see why this idea pops up everywhere in math.... see moreTry the questions and watch how simple number rules turn into fun little surprises.
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2) The next number after 37 that leaves a remainder of 2 when divided by 5 is __

Explanation

37+5=42; 42 mod 5 = 2.

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3) A music playlist has 10 songs. If you listen to 37 songs in a row, which song do you end on?

Explanation

37 mod 10 = 7 → song 7.

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4) When you divide 45 by 7, what is the remainder?

Explanation

7 × 6 = 42; 45 − 42 = 3; remainder = 3.

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5) When 26 is divided by 8, the remainder is 2.

Explanation

8 × 3 = 24; 26 − 24 = 2; remainder = 2.

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6) When 55 is divided by 9, the remainder is __

Explanation

9 × 6 = 54; 55 − 54 = 1.

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7) What is the remainder when 64 is divided by 10?

Explanation

The last digit of 64 is 4, so remainder = 4.

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8) Which numbers leave a remainder of 1 when divided by 5?

Explanation

6−5=1; 10÷5=2 (rem 0); 11−10=1; 16−15=1.

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9) If 23 ≡ 5 (mod 9), which of the following is also true?

Explanation

41−23=18 → divisible by 9 → same remainder.

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10) Every multiple of 4 leaves a remainder of 0 when divided by 4.

Explanation

Multiples divide evenly → remainder 0.

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11) When 120 is divided by 11, the remainder is __

Explanation

11×10=110; 120−110=10.

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12) If a ≡ 3 (mod 5) and b ≡ 4 (mod 5), then (a + b) mod 5 = ?

Explanation

(3+4) mod 5 = 7 mod 5 = 2.

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13) Select all statements that are true.

Explanation

All statements true as per division remainders.

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14) A clock shows 10:00. What time will it show after 19 hours?

Explanation

19 mod 12 = 7; 10+7=17 → 5:00.

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15) When 99 is divided by 9, the remainder is __

Explanation

9×11=99; remainder 0.

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16) Numbers ending in 0 always have a remainder of 0 when divided by 5.

Explanation

Multiples of 5 ending in 0 divide evenly.

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17) Which property is true for all modulo operations?

Explanation

Both hold true for modular arithmetic.

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18) Which numbers leave a remainder of 3 when divided by 4?

Explanation

3 mod 4 = 3; 7−4=3; 11−8=3.

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19) When 200 is divided by 9, the remainder is __

Explanation

9×22=198; 200−198=2.

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20) A carousel has 18 seats. If 95 people take rides one after another, which seat does the 95th person sit in?

Explanation

95 mod 18 = 5; seat 5.

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If two numbers have the same remainder when divided by n, they are...
The next number after 37 that leaves a remainder of 2 when divided by...
A music playlist has 10 songs. If you listen to 37 songs in a row,...
When you divide 45 by 7, what is the remainder?
When 26 is divided by 8, the remainder is 2.
When 55 is divided by 9, the remainder is __
What is the remainder when 64 is divided by 10?
Which numbers leave a remainder of 1 when divided by 5?
If 23 ≡ 5 (mod 9), which of the following is also true?
Every multiple of 4 leaves a remainder of 0 when divided by 4.
When 120 is divided by 11, the remainder is __
If a ≡ 3 (mod 5) and b ≡ 4 (mod 5), then (a + b) mod 5 = ?
Select all statements that are true.
A clock shows 10:00. What time will it show after 19 hours?
When 99 is divided by 9, the remainder is __
Numbers ending in 0 always have a remainder of 0 when divided by 5.
Which property is true for all modulo operations?
Which numbers leave a remainder of 3 when divided by 4?
When 200 is divided by 9, the remainder is __
A carousel has 18 seats. If 95 people take rides one after another,...
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