Properties of Modular Addition

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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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| Questions: 10 | Updated: Dec 9, 2025
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1) Which property is true for modular addition?

Explanation

Modular addition follows both associative and commutative properties.

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About This Quiz
Properties Of Modular Addition - Quiz

Modular addition follows some neat rules—just like regular arithmetic, it’s commutative and associative, but with remainders built in. In this quiz, you’ll explore how these properties work, test shortcuts for simplifying modular sums, and see why they make problem-solving easier. We bring you this quiz so you can go beyond... see morethe basics and recognize the structure behind modular addition.
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2)
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2) If X ≡ 4 (Mod 6), What Is (X + 10) Mod 6?

Explanation

4 + 10 = 14 → 14 mod 6 = 2.

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3) Compute: (8 + 17 + 22) Mod 9

Explanation

47 mod 9 = 2

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4) Which Is Congruent To (15 + 30) Mod 12?

Explanation

45 mod 12 = 9

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5) If A ≡ 2 (Mod 7) And B ≡ 6 (Mod 7), Then A + B ≡ ? (Mod 7)

Explanation

2 + 6 = 8 → 8 mod 7 = 1

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6) Compute: (90 + 45) Mod 11

Explanation

135 mod 11 = 3

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7) Which Is Equivalent To (23 + 37) Mod 8?

Explanation

60 mod 8 = 4.

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8) If X ≡ 3 (Mod 4), Then (X + 7) Mod 4 = ?

Explanation

3 + 7 = 10 → 10 mod 4 = 2

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9) Simplify: (125 + 250) Mod 15

Explanation

375 mod 15 = 0.

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10) Which rule describes modular addition correctly?

Explanation

Mod operation always keeps the remainder.

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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 property is true for modular addition?
If X ≡ 4 (Mod 6), What Is (X + 10) Mod 6?
Compute: (8 + 17 + 22) Mod 9
Which Is Congruent To (15 + 30) Mod 12?
If A ≡ 2 (Mod 7) And B ≡ 6 (Mod 7), Then A + B ≡ ?...
Compute: (90 + 45) Mod 11
Which Is Equivalent To (23 + 37) Mod 8?
If X ≡ 3 (Mod 4), Then (X + 7) Mod 4 = ?
Simplify: (125 + 250) Mod 15
Which rule describes modular addition correctly?
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