Addition Properties Worksheets - Free Printable

Let's solve each problem on the worksheet step by step and identify the property of addition used in each case.

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1) 2 + 1 = ________

- Answer: 3
- Property: Commutative Property
(But wait — this is just a simple sum. The commutative property would be shown as 2 + 1 = 1 + 2, which isn't what’s written here.)

Actually, since it's just asking to find the sum and identify the property used, we should look at whether the equation shows a specific property.

Let’s analyze each one carefully:

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1) 2 + 1 = ________

- Sum: 3
- Property: This is just a basic addition. No rearrangement or grouping.
- But if we're supposed to recognize a property, perhaps there's a typo or misunderstanding.

Wait — let’s look at the rest.

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2) 5 + 4 = 7 + ________

- Left side: 5 + 4 = 9
- So: 9 = 7 + ? → ? = 2
- Answer: 2
- Now, check: 5 + 4 = 7 + 2 → 9 = 9 ✔
- But this is not a standard property like commutative or associative.
- However, notice that:
- 5 + 4 = 9
- 7 + 2 = 9
- This is not showing a property of addition directly unless it's meant to show equality, but no standard property is being demonstrated.

Wait — maybe this is a trick. Let's go to the next ones.

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3) (3 + 3) + 6 = ________

- First: 3 + 3 = 6
- Then: 6 + 6 = 12
- So: 12

Now:
9 + (3 + 6) = ________
- 3 + 6 = 9
- 9 + 9 = 18? Wait — no:
- 9 + (3 + 6) = 9 + 9 = 18

Wait — but the first expression was (3+3)+6 = 6+6=12
Second is 9+(3+6)=9+9=18 — not equal.

But the worksheet says:
> (3 + 3) + 6 = ________
> 9 + (3 + 6) = ________

This seems inconsistent. Let's double-check.

Wait — maybe it's a typo?

Look again:

> 3) (3 + 3) + 6 = ________
> 9 + (3 + 6) = ________

But (3+3)+6 = 6+6 = 12
And 9 + (3+6) = 9 + 9 = 18 → not equal

So unless there's a mistake in the problem, this doesn’t make sense.

Wait — perhaps the second line is meant to be:
> (3 + 3) + 6 = 3 + (3 + 6)

That would make sense for Associative Property.

But instead, it says:
> 9 + (3 + 6)

Which is different.

Wait — perhaps the number "9" is a typo?

Let’s assume it's a typo and it should be:
> 3 + (3 + 6) = ?

Then:
- (3+3)+6 = 6+6 = 12
- 3+(3+6) = 3+9 = 12 → same

Then property: Associative Property

But the worksheet says:
> 9 + (3 + 6) = ?

That’s confusing.

Alternatively, maybe the first line is:
> (3 + 3) + 6 = 6 + 6 = 12
> 9 + (3 + 6) = 9 + 9 = 18

Not equal → so not a property.

Wait — maybe the “9” is actually meant to be “3”? That would make sense.

Let me re-express:

Possibly, the intended problem is:
> (3 + 3) + 6 = ________
> 3 + (3 + 6) = ________

Then both are 12 → Associative Property

But it says "9 + (3 + 6)", which is not matching.

Unless... is the "9" from 3+3+6? No.

Wait — perhaps the first line is:
> (3 + 3) + 6 = 6 + 6 = 12
> And then 9 + (3 + 6) = 9 + 9 = 18 — but that's unrelated.

I think there may be an error in the worksheet.

But let’s move on.

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4) 10 + 5 = ________

- Sum: 15
- Then: 10 + 5 = ________
- Same thing — 15
- But then it says: 10 + 5 = ________ → already done
- Then it asks: Property?

No change — just repetition.

Unless it's comparing to 5 + 10?

But it doesn't say that.

Wait — maybe the second line is meant to be:
> 5 + 10 = ________

Then it would be 15, and the property would be Commutative Property

But it says: 10 + 5 = ________ — same as above.

So probably not.

Wait — perhaps the problem is:

> 10 + 5 = ________
> 10 + 5 = ________

Same thing — no property shown.

But then it says "Property:" — so likely, it's missing something.

Let’s look at the original image description.

Wait — I don't have the image, but based on your text:

> 4) 10 + 5 = ________
> 10 + 5 = ________
> Property: ________

That’s redundant.

Perhaps it's supposed to be:
> 10 + 5 = 5 + 10 = ________

Then it would be 15, and property: Commutative

But it’s not written that way.

Maybe the second line is:
> 5 + 10 = ________

Then it makes sense.

Given that, I suspect some typos.

Let’s try to reconstruct based on common properties.

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Let's re-analyze with correct assumptions:

#### 1) 2 + 1 = 3
- Sum: 3
- Property: None shown — just basic addition.

But perhaps the idea is that 2 + 1 = 1 + 2, but it’s not stated.

So maybe skip.

#### 2) 5 + 4 = 7 + ?
- 5 + 4 = 9
- 7 + ? = 9 → ? = 2
- So: 5 + 4 = 7 + 2
- But this is not a property — it's just equality.

Unless it's meant to be Addition Property of Equality or something, but not a standard property of addition.

Wait — perhaps it's showing the idea of balancing, but not a named property.

Alternatively, maybe it's testing additive identity or zero, but no zero here.

Not helpful.

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#### 3) (3 + 3) + 6 = 6 + 6 = 12
> 9 + (3 + 6) = 9 + 9 = 18

Wait — unless the "9" is a typo and it's supposed to be 3?

Try:
> (3 + 3) + 6 = 3 + (3 + 6) = 3 + 9 = 12

Then both sides equal 12 → Associative Property

Yes! That makes sense.

So likely, the second line is 3 + (3 + 6), not 9 + (3 + 6)

Probably a typo in transcription.

Assume:
> (3 + 3) + 6 = 12
> 3 + (3 + 6) = 12
> Property: Associative Property

✔

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#### 4) 10 + 5 = 15
> 5 + 10 = 15
> Property: Commutative Property

But in the worksheet, it says:
> 10 + 5 = ________
> 10 + 5 = ________

Still the same.

But if the second line is 5 + 10, then it's commutative.

So likely, it's meant to be:
> 10 + 5 = 15
> 5 + 10 = 15
> Property: Commutative Property

We'll assume that.

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#### 5) 7 + 3 = 10
> 3 + 7 = 10
> Property: Commutative Property

Yes — order changed.

✔

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#### 6) (1 × 5) + 3 = ?

Wait — multiplication? But it's a Properties of Addition worksheet.

(1 × 5) = 5, then +3 = 8

Then:
> 1 + (5 + 3) = 1 + 8 = 9

But 5 + 3 = 8 ≠ 9

Wait — unless it's:
> (1 + 5) + 3 = 6 + 3 = 9
> 1 + (5 + 3) = 1 + 8 = 9

Ah! So likely, it's:
> (1 + 5) + 3 = 9
> 1 + (5 + 3) = 9
> Property: Associative Property

But in the worksheet, it says:
> (1 × 5) + 3 = ?

That’s multiplication — not addition.

So probably a typo.

Likely, it should be:
> (1 + 5) + 3 = ________
> 1 + (5 + 3) = ________

Then both = 9 → Associative Property

We’ll assume that.

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#### 7) (10 + 7) + 8 = ?
- 10 + 7 = 17
- 17 + 8 = 25

Then:
> 10 + (7 + 8) = 10 + 15 = 25

So:
> (10 + 7) + 8 = 25
> 10 + (7 + 8) = 25
> Property: Associative Property

✔

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#### 8) 4 + 2 = 6
> 2 + 4 = 6
> Property: Commutative Property

✔

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Final Answers (with corrections assumed):

| Problem | Answer | Property |
|--------|--------|----------|
| 1) 2 + 1 = ? | 3 | None (or basic addition) |
| 2) 5 + 4 = 7 + ? | 2 | Not a standard property (but 5+4=9, 7+2=9) |
| 3) (3+3)+6 = ?<br>9 + (3+6) = ? | 12<br>18 | Likely typo — should be 3 + (3+6) → Associative |
| 4) 10 + 5 = ?<br>10 + 5 = ? | 15<br>15 | Likely typo — should be 5 + 10 → Commutative |
| 5) 7 + 3 = ?<br>3 + 7 = ? | 10<br>10 | Commutative Property |
| 6) (1×5)+3 = ?<br>1+(5+3) = ? | 8<br>9 | Likely typo — should be (1+5)+3 → Associative |
| 7) (10+7)+8 = ?<br>10+(7+8) = ? | 25<br>25 | Associative Property |
| 8) 4 + 2 = ?<br>2 + 4 = ? | 6<br>6 | Commutative Property |

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Corrected Version (assuming typos):

Let’s write the corrected version:

1) 2 + 1 = 3
Property: None (basic addition)

2) 5 + 4 = 7 + 2
Property: Not a standard property — just equivalent sums

3) (3 + 3) + 6 = 12
3 + (3 + 6) = 12
Property: Associative Property

4) 10 + 5 = 15
5 + 10 = 15
Property: Commutative Property

5) 7 + 3 = 10
3 + 7 = 10
Property: Commutative Property

6) (1 + 5) + 3 = 9
1 + (5 + 3) = 9
Property: Associative Property

7) (10 + 7) + 8 = 25
10 + (7 + 8) = 25
Property: Associative Property

8) 4 + 2 = 6
2 + 4 = 6
Property: Commutative Property

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Summary of Properties Used:

- Commutative Property: Order doesn't matter: a + b = b + a
→ Problems 4, 5, 8

- Associative Property: Grouping doesn't matter: (a + b) + c = a + (b + c)
→ Problems 3, 6, 7

- Problem 1 and 2 are either basic or not demonstrating a named property.

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Final Answer:

Here’s the completed worksheet (corrected):

```
1) 2 + 1 = 3 Property: None
2) 5 + 4 = 7 + 2 Property: None (equivalent sums)
3) (3 + 3) + 6 = 12 Property: Associative
3 + (3 + 6) = 12
4) 10 + 5 = 15 Property: Commutative
5 + 10 = 15
5) 7 + 3 = 10 Property: Commutative
3 + 7 = 10
6) (1 + 5) + 3 = 9 Property: Associative
1 + (5 + 3) = 9
7) (10 + 7) + 8 = 25 Property: Associative
10 + (7 + 8) = 25
8) 4 + 2 = 6 Property: Commutative
2 + 4 = 6
```

> Note: Some problems in the original sheet appear to have typos (e.g., "9 + (3+6)" instead of "3 + (3+6)", and "1 × 5" instead of "1 + 5"). These were corrected to match standard properties.

Let me know if you'd like a printable version or explanation for students!