Properties of Addition Worksheets with Answer Key - Free Printable

Let's solve the Properties of Addition Worksheet step by step.

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Part A: Identify the property of addition for each.

We are given four examples and need to identify which property applies.

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1) 7 + 3 = 3 + 7

- The order of numbers is switched.
- This matches the Commutative Property:
$ a + b = b + a $

✔ Answer: Commutative Property

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2) 8 + (-8) = 0

- A number added to its negative gives zero.
- This is the Inverse Property:
$ a + (-a) = 0 $

✔ Answer: Inverse Property

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3) 4 + 0 = 4

- Adding zero to a number doesn’t change it.
- This is the Identity Property:
$ a + 0 = a $

✔ Answer: Identity Property

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4) (9 + 3) + 6 = 9 + (3 + 6)

- The grouping of numbers changes, but the order stays the same.
- This matches the Associative Property:
$ (a + b) + c = a + (b + c) $

✔ Answer: Associative Property

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✔ Part A Answers:

1. Commutative Property
2. Inverse Property
3. Identity Property
4. Associative Property

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Part B: Write the answers and the addition properties for the following

Now we compute each expression and state the property used.

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1) 9 + 0 = ?

- $ 9 + 0 = 9 $
- Adding zero → Identity Property

✔ Answer: $ 9 $, Identity Property

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2) 3 + 12 = ?

- $ 3 + 12 = 15 $
- No special grouping or zero involved; just basic addition.
- But since it's just two numbers being added, no specific property is required unless specified.
- However, if we're identifying a property, this is just an example of addition, but no specific property is highlighted here unless we assume commutative (but not applied).
- Since it's not rearranged, grouped, or involving zero/negative, it's just basic addition.
- But in context, we might say it’s not using any special property, or just Addition.

But let's consider: If we're asked to write the property, and none is explicitly shown, then perhaps we just write the answer and note that it's not demonstrating a special property.

However, often in such worksheets, they expect you to recognize that any addition follows general rules, but only when a property is demonstrated do we name it.

So:

✔ Answer: $ 15 $, No specific property (or just Addition)

But wait — maybe they want us to recognize that it could be commutative, but it's written as is.

Actually, since there's no rearrangement, grouping, zero, or inverse, no special property is demonstrated.

So best to write:

✔ Answer: $ 15 $, None (or Basic Addition)

But let’s check others.

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3) 0 + 13 = ?

- $ 0 + 13 = 13 $
- Zero is added → Identity Property

✔ Answer: $ 13 $, Identity Property

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4) 18 + 3 = ?

- $ 18 + 3 = 21 $
- Again, just simple addition.
- No special property shown.

✔ Answer: $ 21 $, None (or Basic Addition)

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5) 10 + (-10) = ?

- $ 10 + (-10) = 0 $
- A number plus its opposite → Inverse Property

✔ Answer: $ 0 $, Inverse Property

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6) (15 + 2) + 1 = ?

- First: $ 15 + 2 = 17 $, then $ 17 + 1 = 18 $
- So total: $ (15 + 2) + 1 = 18 $
- Grouping is used → Associative Property
- But note: It’s not rewritten as $ 15 + (2 + 1) $, so it's just showing how grouping works.

Even though it's not re-grouped, the expression uses parentheses to group first, so it demonstrates grouping, hence Associative Property.

✔ Answer: $ 18 $, Associative Property

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✔ Part B Final Answers:

| Problem | Answer | Property |
|--------|--------|----------|
| 1) 9 + 0 | 9 | Identity Property |
| 2) 3 + 12 | 15 | None / Basic Addition |
| 3) 0 + 13 | 13 | Identity Property |
| 4) 18 + 3 | 21 | None / Basic Addition |
| 5) 10 + (-10) | 0 | Inverse Property |
| 6) (15 + 2) + 1 | 18 | Associative Property |

> Note: For problems 2 and 4, since no special property is demonstrated (no zero, no negative, no regrouping), we can simply say "No specific property" or leave it blank. But in many educational contexts, they might accept "Addition" or omit the property.

However, if the worksheet expects a property for every one, perhaps they expect Commutative for 2 and 4? But that’s not correct because commutative would involve switching order (e.g., 3+12 = 12+3).

Since the expressions are written in standard form, no property is being demonstrated.

So safest:

- 2) 15, None
- 4) 21, None

Alternatively, if the instruction says “write the addition properties”, and all must have one, maybe they expect Commutative or Associative, but that would be incorrect.

So better to stick with accurate identification.

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✔ Final Answer Summary:

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A) Identify the property:

1. Commutative Property
2. Inverse Property
3. Identity Property
4. Associative Property

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B) Write answers and properties:

1. $ 9 + 0 = 9 $, Identity Property
2. $ 3 + 12 = 15 $, None (or Basic Addition)
3. $ 0 + 13 = 13 $, Identity Property
4. $ 18 + 3 = 21 $, None (or Basic Addition)
5. $ 10 + (-10) = 0 $, Inverse Property
6. $ (15 + 2) + 1 = 18 $, Associative Property

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