Properties of Addition Worksheets with Answer Key - Free Printable

Let’s solve each part step by step.

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Part A: Identify the property of addition for each.

We’ll match each equation to one of the four properties from the table:

1. 7 + 3 = 3 + 7
→ The order of numbers is switched, but the sum stays the same.
→ This matches the Commutative Property: a + b = b + a

2. 8 + (-8) = 0
→ A number added to its negative gives zero.
→ This matches the Inverse Property: a + (-a) = 0

3. 4 + 0 = 4
→ Adding zero doesn’t change the number.
→ This matches the Identity Property: a + 0 = a

4. (9 + 3) + 6 = 9 + (3 + 6)
→ The grouping changes, but the sum stays the same.
→ This matches the Associative Property: (a + b) + c = a + (b + c)

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

We’ll calculate the answer first, then name the property used.

1. 9 + 0 = ?
→ Answer: 9
→ Property: Identity Property (adding zero)

2. 3 + 12 = ?
→ Answer: 15
→ Property: Commutative Property? Wait — actually, this is just basic addition. But since we’re asked to name an *addition property*, and no special rule like identity or inverse is shown here, it’s likely testing if you know that addition can be done in any order — so even though it’s written as 3+12, you could think of it as 12+3. So we’ll say Commutative Property applies because order doesn’t matter.

Actually — let’s double-check: The problem says “write the answers AND the addition properties”. For simple sums like 3+12, unless there’s a zero or negatives or parentheses, the only relevant property might be commutative — but technically, every addition uses the idea that numbers can be combined — but since the worksheet focuses on those 4 properties, and this isn’t identity, inverse, or associative, the best fit is Commutative Property — because you could also write 12 + 3 and get the same result.

However — wait! Looking back at Part A, they didn’t ask for properties on plain sums — only when a specific property was demonstrated. In Part B, question 2 is just “3 + 12 =” — no rearrangement or grouping shown. Hmm.

Let’s look again at the instructions: “Write the answers and the addition properties for the following”

Maybe for some, no special property is being demonstrated — but the worksheet expects us to pick the most relevant one from the 4.

Actually — perhaps for #2 and #4, since they are straightforward additions without zeros, negatives, or groupings, maybe they don’t demonstrate a specific property beyond basic addition — but that doesn’t fit the task.

Alternatively — maybe the teacher wants us to recognize that even simple addition relies on these properties implicitly.

Let’s check standard practice: In many worksheets, if you see something like “3 + 12”, and you’re to name a property, and none of the special ones apply directly, sometimes they expect “none” — but that’s not among the options.

Wait — looking at the original table, all four properties are defined. For 3 + 12, since it’s just adding two numbers, and no special form, perhaps it’s not demonstrating a particular property — BUT — notice that in Part A, they gave examples where the property was clearly visible (like switching order, or adding zero).

Perhaps for #2 and #4, since they are just computing sums, and no property is explicitly shown, we should still compute the answer, and for property, maybe leave blank? But the line is there.

Another thought: Maybe for #2, since 3 + 12 is the same as 12 + 3, we can say Commutative Property applies — even if not rewritten.

Similarly, for #4: 18 + 3 — same thing.

But let’s compare with #6: (15 + 2) + 1 — that has parentheses, so Associative Property will apply.

And #5: 10 + (-10) — that’s Inverse.

#1 and #3 have zero — Identity.

So for #2 and #4, since they are just plain addition, perhaps the intended answer is that they use the Commutative Property implicitly — because addition is commutative.

I think that’s safe.

So:

2. 3 + 12 = 15 → Commutative Property (since order doesn't matter)

But wait — actually, in many curricula, when they ask for the property for a simple sum like this, and no transformation is shown, they might not expect a property — but since the worksheet forces it, and given that commutative is the most general, we'll go with that.

Alternatively — perhaps for #2 and #4, no specific property is being illustrated, so maybe we should write "None" — but that’s not in the list.

Looking back at the user’s image — in Part B, for example, #1 is 9+0 — which is clearly Identity. #5 is 10 + (-10) — Inverse. #6 has parentheses — Associative.

For #2: 3+12 — no zero, no negative, no parentheses — so perhaps it's just testing computation, and the property is not applicable — but the worksheet says "write the addition properties", implying one of the four.

I recall that in some textbooks, they consider that every addition operation assumes the commutative and associative properties, but for identification purposes, we only name the property that is visibly demonstrated.

In this case, for 3+12, nothing is visibly demonstrating a property — it's just a sum.

But let's look at the structure: In Part A, they had equations that matched the properties exactly. In Part B, for items like #1, #3, #5, #6, the property is clear. For #2 and #4, perhaps they want us to realize that addition is commutative, so even though it's written as 3+12, it equals 12+3, so Commutative Property.

I think that's the intended answer.

Similarly for #4: 18+3 — same thing.

So I'll proceed with that.

3. 0 + 13 = ?
→ Answer: 13
→ Property: Identity Property (adding zero)

4. 18 + 3 = ?
→ Answer: 21
→ Property: Commutative Property (order doesn't matter)

5. 10 + (-10) = ?
→ Answer: 0
→ Property: Inverse Property

6. (15 + 2) + 1 = ?
→ First, 15 + 2 = 17, then 17 + 1 = 18
→ Or, using associative property: 15 + (2 + 1) = 15 + 3 = 18
→ Property: Associative Property

Now, let’s write down all answers clearly.

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Final Answer:

A) Identify the property:

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

B) Write answers and properties:

1. 9 + 0 = 9 — Identity Property
2. 3 + 12 = 15 — Commutative Property
3. 0 + 13 = 13 — Identity Property
4. 18 + 3 = 21 — Commutative Property
5. 10 + (-10) = 0 — Inverse Property
6. (15 + 2) + 1 = 18 — Associative Property