Properties of Modulo

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Questions: 10 | Updated: Jan 20, 2026
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1) Which of the following is true?

Explanation

17≡2(mod5) (diff 15) and 22≡1(mod7) (diff 21).

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About This Quiz
Properties Of Modulo - Quiz

Modular arithmetic isn’t just about finding leftovers — it follows clever rules that make problem solving easier. In this quiz, you’ll learn how addition, multiplication, and congruences behave under modulo and why those patterns matter. We bring you this quiz to help you move beyond basics and into deeper modula... see morereasoning.
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2) Which statement is correct about 12 mod 6?

Explanation

12≡6(mod6) and 12≡0(mod6)  (both diffs are multiples of 6).

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3) Which statement is correct about 12 mod 6?

Explanation

The modulo operation finds the remainder of division of one number by another. In this case, 12 divided by 6 equals 2 with a remainder of 0. Therefore, 12 mod 6 is 0.

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4) If x ≡ 4 (mod 7), what is 2x mod 7?

Explanation

2⋅4=8≡1(mod7).

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5) Which is true about modulo arithmetic?

Explanation

That’s exactly what “mod” returns.

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6) If a ≡ 5 (mod 6) and b ≡ 4 (mod 6), what is a m b (mod 6)?

Explanation

5⋅4=20≡2(mod6)5\cdot4=20\equiv \mathbf{2}\pmod65⋅4=20≡2(mod6).

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

Explanation

41−5=36 is a multiple of 9.

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8) Which is equivalent to 29 mod 6?

Explanation

29=6×4+5.

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9) If 16 ≡ 1 (mod 5), then 3 m 16 ≡ ? (mod 5)

Explanation

3⋅1=3(mod5).

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10) Which is a property of mod arithmetic?

Explanation

Addition and multiplication both distribute over mod.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Which of the following is true?
Which statement is correct about 12 mod 6?
Which statement is correct about 12 mod 6?
If x ≡ 4 (mod 7), what is 2x mod 7?
Which is true about modulo arithmetic?
If a ≡ 5 (mod 6) and b ≡ 4 (mod 6), what is a m b (mod 6)?
If 23 ≡ 5 (mod 9), which of the following is also true?
Which is equivalent to 29 mod 6?
If 16 ≡ 1 (mod 5), then 3 m 16 ≡ ? (mod 5)
Which is a property of mod arithmetic?
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