Commutative or Associative Property? | 3rd Grade Math Worksheets - Free Printable

It looks like you've uploaded an image of a math worksheet titled "Identify the Property: Commutative or Associative?". The task is to determine whether each given equation demonstrates the Commutative Property or the Associative Property of addition or multiplication.

Let’s go through each problem step by step and identify the correct property, then explain why.

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🔹 Definitions:

- Commutative Property:
- Addition: $ a + b = b + a $
- Multiplication: $ a \times b = b \times a $
→ Order changes, but result stays the same.

- Associative Property:
- Addition: $ (a + b) + c = a + (b + c) $
- Multiplication: $ (a \times b) \times c = a \times (b \times c) $
→ Grouping changes, but order stays the same.

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Now let's analyze each problem:

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A) $ 2 + (8+4) = (2+8) + 4 $

- Left side: $ 2 + (8+4) = 2 + 12 = 14 $
- Right side: $ (2+8) + 4 = 10 + 4 = 14 $
- The grouping changed: from $ (8+4) $ to $ (2+8) $
- Numbers are in the same order, just grouped differently.

✔ Answer: Associative Property

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B) $ (7×5) + 6 = 6 + (7×5) $

- Left: $ 35 + 6 = 41 $
- Right: $ 6 + 35 = 41 $
- The order of addition changed: $ 35 + 6 $ vs $ 6 + 35 $
- The addends were swapped.

✔ Answer: Commutative Property

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C) $ (5×8) + 2 = (8×5) + 2 $

- Left: $ 40 + 2 = 42 $
- Right: $ 40 + 2 = 42 $
- Inside the parentheses: $ 5×8 $ became $ 8×5 $
- This is swapping the order of multiplication.

✔ Answer: Commutative Property (of multiplication)

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D) $ 2 + (6×8) = (6×8) + 2 $

- Left: $ 2 + 48 = 50 $
- Right: $ 48 + 2 = 50 $
- The order of addition changed: $ 2 + 48 $ vs $ 48 + 2 $

✔ Answer: Commutative Property

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E) $ (8×7) + 4 = 8 + (7×4) $

Wait — let's check this carefully.

Left: $ (8×7) + 4 = 56 + 4 = 60 $
Right: $ 8 + (7×4) = 8 + 28 = 36 $

✘ Not equal! So this equation is not true.

But wait — the problem says “identify the property” — so perhaps it's a trick question?

Let’s recheck the original expression:

> E) $ (8×7) + 4 = 8 + (7×4) $

This is not a valid identity because:
- $ 56 + 4 = 60 $
- $ 8 + 28 = 36 $
- $ 60 ≠ 36 $

So this does not represent either commutative or associative property correctly.

➡️ Conclusion: This equation is false, so it does not demonstrate either property.

But since the instruction says "write A or C", we must assume the equation is intended to be valid.

Possibility: There might be a typo.

Alternatively, maybe it was meant to be:

> $ (8×7) + 4 = (7×8) + 4 $ → That would be commutative.

But as written, it's invalid.

So unless there's a mistake in the worksheet, E is not a valid example of either property.

But let’s suppose the problem expects us to ignore truth and just look at form.

Still, the right-hand side changes both multiplication order and addition order — it's not consistent.

So likely, this one is incorrect.

But let’s move on.

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F) $ 11 + (8×8) = 11 + (8×8) $

- Both sides are identical.
- No change in order or grouping.

→ This is just reflexive or identity, not commutative or associative.

But since it's the same on both sides, it doesn't show any transformation.

So no property is demonstrated here.

But again, if it's asking for a property, and nothing changed, it's not applicable.

Possibly a typo.

Wait — maybe it's supposed to be:

> $ 11 + (8×8) = (8×8) + 11 $

Then it would be commutative.

As written, it's just equal to itself — no property shown.

So likely, F is invalid or missing a change.

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G) $ (7×2) + 6 = 7 + (2×6) $

Check values:

Left: $ 14 + 6 = 20 $
Right: $ 7 + 12 = 19 $ → Not equal

So again, false.

No property applies.

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H) $ 12 + (8×1) = (12×8) + 1 $

Left: $ 12 + 8 = 20 $
Right: $ 96 + 1 = 97 $ → Not equal

False.

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I) $ 2 + (3×8) = (3×8) + 2 $

Left: $ 2 + 24 = 26 $
Right: $ 24 + 2 = 26 $

Same as D — just switching order of addition.

✔ Answer: Commutative Property

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J) $ 2×(3×8) = (2×3)×8 $

Left: $ 2 × 24 = 48 $
Right: $ 6 × 8 = 48 $

Grouping changed: $ (3×8) $ vs $ (2×3) $

Order of numbers: 2, 3, 8 — all same, just regrouped.

This is Associative Property of Multiplication

✔ Answer: Associative Property

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K) $ (8×7) + 4 = 8 + (7×4) $ ← Same as E — false

We already saw this is false.

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L) $ (8×8) + 4 = 8 + (8×4) $

Left: $ 64 + 4 = 68 $
Right: $ 8 + 32 = 40 $ → Not equal

False.

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Wait — looking back, only A, B, C, D, I, J seem valid.

Let’s list only the ones that are correctly demonstrating a property:

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✔ Final Answers:

| Letter | Equation | Property |
|--------|---------|----------|
| A | $ 2 + (8+4) = (2+8) + 4 $ | Associative |
| B | $ (7×5) + 6 = 6 + (7×5) $ | Commutative |
| C | $ (5×8) + 2 = (8×5) + 2 $ | Commutative |
| D | $ 2 + (6×8) = (6×8) + 2 $ | Commutative |
| I | $ 2 + (3×8) = (3×8) + 2 $ | Commutative |
| J | $ 2×(3×8) = (2×3)×8 $ | Associative |

Others (E, F, G, H, K, L) are either false or not showing a property.

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🟩 Summary of Answers:

- A: Associative
- B: Commutative
- C: Commutative
- D: Commutative
- E: ✘ Invalid (not true)
- F: ✘ Identical (no property)
- G: ✘ Invalid
- H: ✘ Invalid
- I: Commutative
- J: Associative
- K: ✘ Invalid
- L: ✘ Invalid

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✔ Correct Answers to Fill In:

Assuming the worksheet expects answers for all letters, but some may have typos.

If we go strictly by what makes sense:

- A: A
- B: C
- C: C
- D: C
- E: ✘ (but if forced, maybe C? But it's wrong)
- F: ✘
- G: ✘
- H: ✘
- I: C
- J: A
- K: ✘
- L: ✘

But since the student is to write A or C, and many equations are invalid, it's possible there are errors in the worksheet.

However, based on correct mathematical reasoning, here are the valid answers:

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✔ Final Answer Key (Only Valid Ones):

- A: A
- B: C
- C: C
- D: C
- I: C
- J: A

Others are not valid examples.

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If you're filling out the worksheet, write:

- A: A
- B: C
- C: C
- D: C
- E: ✘ (but if required, perhaps leave blank or mark as invalid)
- F: ✘
- G: ✘
- H: ✘
- I: C
- J: A
- K: ✘
- L: ✘

But if the worksheet assumes all are valid, then likely some equations are misprinted.

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💡 Tip:

Double-check the equations — especially E, G, H, K, L — they appear to be incorrectly stated.

For example:
- E: Should be $ (8×7)+4 = (7×8)+4 $ → Commutative
- J: Is correct — Associative
- I: Correct — Commutative

So the worksheet may have typos.

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Let me know if you want a corrected version of the worksheet or help with a specific part!