Algebraic Proofs of Divisibility

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| Questions: 15 | Updated: Oct 14, 2025
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1) A number leaves a remainder of 2 when divided by 5. Which equation represents this situation?

Explanation

When a number n is divided by 5 and leaves a remainder of 2, it can be expressed in the form of 5k + 2, where k is an integer. This means that n is 2 more than a multiple of 5, which corresponds to option C.

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About This Quiz
Algebraic Proofs Of Divisibility - Quiz

Numbers follow patterns, and algebra is the key to proving them! In this quiz, you’ll use algebraic expressions like n = 2k and n = 3k to show when numbers are divisible by 2, 3, 5, 9, and more. You’ll also explore how equations can represent all even, odd, o... see moremultiple-based numbers. We bring you this quiz to strengthen your proof skills and connect arithmetic rules with algebra. see less

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2) A number n is divisible by 4. Which equation represents this?

Explanation

If n is divisible by 4, it can be expressed as 4k because it is exactly 4 times some integer k with no remainder.

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3) A number is divisible by 12 if it is divisible by:

Explanation

A number is divisible by 12 if it is divisible by both 3 and 4, since 12 = 3 × 4.

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4) Which algebraic form shows all even numbers?

Explanation

Even numbers can be represented as 2n because they are multiples of 2.

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5) Which equation models all numbers divisible by both 2 and 5?

Explanation

Numbers divisible by both 2 and 5 must be multiples of their least common multiple, 10, so they can be written as 10n.

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6) A number divided by 7 leaves a remainder of 4. Which equation models this?

Explanation

When a number is divided by 7 and leaves a remainder of 4, it can be expressed as 7k + 4, meaning it is 4 more than a multiple of 7.

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7) Solve for x: 3(x + 4) = 2(x + 7)

Explanation

Solving 3(x + 4) = 2(x + 7): expand to 3x + 12 = 2x + 14, so x = 2.

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8) Solve for x: 4x + 5 = 2x + 15

Explanation

Solving 4x + 5 = 2x + 15: subtract 2x → 2x = 10 → x = 5.

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9) Solve for x: 5(x − 3) = 3(x − 1)

Explanation

Solving 5(x − 3) = 3(x − 1): expand → 5x − 15 = 3x − 3 → 2x = 12 → x = 6.

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10) Solve for x: 3(x + 2) = 2(x + 8)

Explanation

Solving 3(x + 2) = 2(x + 8): expand → 3x + 6 = 2x + 16 → x = 10.

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11) Solve for x: 2x + 5 = x + 11

Explanation

Solving 2x + 5 = x + 11: subtract x → x = 6.

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12) Which equation represents all numbers divisible by 9?

Explanation

Numbers divisible by 9 can be written as 9 times an integer, so n = 9k.

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13) Which algebraic form shows all odd numbers?

Explanation

Odd numbers are one more than even numbers, so they take the form 2k + 1.

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14) Which equation models all numbers divisible by both 3 and 5?

Explanation

Numbers divisible by both 3 and 5 are multiples of 15, so they can be written as 15n.

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15) If n = 6k, then n is always:

Explanation

If n = 6k, it is a multiple of 6 and therefore divisible by 6.

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A number leaves a remainder of 2 when divided by 5. Which equation...
A number n is divisible by 4. Which equation represents this?
A number is divisible by 12 if it is divisible by:
Which algebraic form shows all even numbers?
Which equation models all numbers divisible by both 2 and 5?
A number divided by 7 leaves a remainder of 4. Which equation models...
Solve for x: 3(x + 4) = 2(x + 7)
Solve for x: 4x + 5 = 2x + 15
Solve for x: 5(x − 3) = 3(x − 1)
Solve for x: 3(x + 2) = 2(x + 8)
Solve for x: 2x + 5 = x + 11
Which equation represents all numbers divisible by 9?
Which algebraic form shows all odd numbers?
Which equation models all numbers divisible by both 3 and 5?
If n = 6k, then n is always:
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