Divisibility Rules and Algebraic Forms

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| Questions: 15 | Updated: Oct 14, 2025
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1) A number is divisible by 2 if:

Explanation

Even numbers are multiples of 2. A number’s divisibility by 2 depends only on its ones digit.

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About This Quiz
Divisibility Rules And Algebraic Forms - Quiz

Ever wondered why divisibility rules really work? In this quiz, you’ll move beyond memorizing shortcuts and actually prove them with examples and equations. From showing why digit sums reveal divisibility to testing algebraic forms for even and odd numbers, you’ll practice connecting number tricks to solid reasoning. Take this quiz... see moreto see how divisibility and proofs come together in middle school math! see less

2) Which number confirms the divisibility rule for 3 (digit sum divisible by 3)?

Explanation

If the sum of digits is a multiple of 3, so is the whole number. 1+2+3=6, a multiple of 3.

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3) A number is divisible by 9 if:

Explanation

Because 10 ≡ 1 (mod 9), so each place value acts like “1,” meaning the digit sum determines divisibility by 9.

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4) If a number ends in 0, it is divisible by:

Explanation

Ending in 0 means it’s a multiple of both 2 and 5 — hence divisible by 10.

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5) A number leaves a remainder of 2 when divided by 5. Which equation represents this situation?

Explanation

The number is two more than a multiple of 5.

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

Explanation

Multiplying any integer by 4 produces a multiple of 4.

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

Explanation

The least common multiple (LCM) of 3 and 4 is 12.

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8) Which algebraic form shows all even numbers?

Explanation

Multiplying any integer by 2 gives an even number.

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

Explanation

The smallest number divisible by 2 and 5 is 10 → multiples of 10 work for both.

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

Explanation

Every such number is 4 more than a multiple of 7.

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

Explanation

3x + 12 = 2x + 14 → x = 2. Linear equation — isolate x.

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

Explanation

Subtract 2x → 2x = 10 → x = 5.

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13) Solve for x: 5(x − 3) = 3(x − 1)

Explanation

5x – 15 = 3x – 3 → 2x = 12 → x = 6.

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

Explanation

3x + 6 = 2x + 16 → x = 10.

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

Explanation

Move x → x = 6.

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A number is divisible by 2 if:
Which number confirms the divisibility rule for 3 (digit sum divisible...
A number is divisible by 9 if:
If a number ends in 0, it is divisible by:
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
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