Math worksheet on properties of mathematics with multiple-choice questions.

Let’s go through each question one by one, carefully analyzing what property is being used or asked for.

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Question 1:
Expression: 3(6 + 5) = 18 + 15
This is multiplying a number (3) by a sum inside parentheses, and then distributing that multiplication to each term inside: 3×6 + 3×5 = 18 + 15.
That’s the Distributive Property.
✔ Correct answer: D

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Question 2:
Expression: (7 + 9) + 5 = 7 + (9 + 5)
Here, the grouping of numbers changes, but the order stays the same. That’s the Associative Property of Addition.
✔ Correct answer: C

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Question 3:
Identity Property of Addition means adding zero doesn’t change the number.
Look at option C: 4 + 0 = 4 → This shows identity.
Option A is commutative, B is associative, D is multiplication identity.
✔ Correct answer: C

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Question 4:
Commutative Property of Addition means you can swap the order: a + b = b + a.
Check each:
A. a + b = b + a → ✔ Commutative
B. 3 + x = x + 3 → ✔ Commutative
C. ab = ba → ✘ This is multiplication, not addition! So this does NOT show commutative property of addition.
D. 3x + 4y = 4y + 3x → ✔ Still addition, just swapped terms — commutative.
So the one that does NOT show it is C.
✔ Correct answer: C

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Question 5:
Which operation won’t change the value of any nonzero number?
A. Dividing by Zero → Undefined! Not allowed.
B. Multiplying by One → Yes! Any number × 1 = itself.
C. Adding One → Changes the number.
D. Multiplying by Zero → Makes everything zero.
✔ Correct answer: B

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Question 6:
3 + 0 = 3 → Adding zero doesn’t change the number. That’s the Identity Property of Addition.
✔ Correct answer: B

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Question 7:
Which does NOT show Commutative Property?
Commutative means order doesn’t matter: a op b = b op a.
A. xy - 9 = xy → This isn’t even comparing two orders — it’s saying subtracting 9 from xy equals xy? That’s false unless 9=0. Also, it’s not about swapping order.
B. yx = xy → ✔ Commutative multiplication
C. x + y = y + x → ✔ Commutative addition
D. 3 + y = y + 3 → ✔ Commutative addition
So A is the odd one out — it’s not even trying to show commutativity.
✔ Correct answer: A

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Question 8:
Expression: (4 × 9) × 8 = 9 × (5 × 4) ← Wait, this looks wrong. Let me check again.

Actually, looking closely:
It says: (4 × 9) × 8 = 9 × (5 × 4) → That can’t be right because 5 wasn’t in the original left side. Probably a typo? But let’s assume it meant:
(4 × 9) × 8 = 4 × (9 × 8) → That would be Associative Property of Multiplication.

But as written: Left side has 4,9,8; right side has 9,5,4 → That’s inconsistent. Maybe it’s supposed to be:
(4 × 9) × 8 = 4 × (9 × 8) → Then it’s Associative.

Alternatively, if it’s (4 × 9) × 8 = 9 × (4 × 8), still associative.

Wait — perhaps it’s a misprint and should be:
(4 × 9) × 8 = 4 × (9 × 8) → Associative Property of Multiplication.

Looking at options:
B. Associative Property of Multiplication → makes sense.

But let’s double-check the image text:
“ (4 x 9) x 8 = 9 x (5 x 4) ” → That must be a typo. Likely meant “(4 x 9) x 8 = 4 x (9 x 8)” or similar.

Given the context and typical questions, they probably meant to show grouping change → Associative Property of Multiplication.

✔ Correct answer: B

*(Note: If we take the equation literally as written, it’s mathematically incorrect — 4×9×8 = 288, while 9×5×4 = 180. So definitely a typo. We go with intent.)*

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Question 9:
3 × (6 + 8) = 3 × 6 + 3 × 8
This is distributing the 3 across the sum → Distributive Property.
✔ Correct answer: B

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Question 10:
(5 + 8) × 7 = 5 × 7 + 8 × 7
Again, multiplying a sum by a number by distributing → Distributive Property.
✔ Correct answer: C

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Now, compiling all answers:

1. D
2. C
3. C
4. C
5. B
6. B
7. A
8. B
9. B
10. C

Final Answer:
1) D
2) C
3) C
4) C
5) B
6) B
7) A
8) B
9) B
10) C