Math worksheet teaching the four properties of addition: commutative, associative, identity, and inverse, with examples and practice problems.

Let’s go through each part step by step.

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Part A: Identify the property of additions for each.

We’re matching equations to the correct addition property from the table at the top.

1. 7 + 3 = 3 + 7
→ This shows that changing the order doesn’t change the sum. That’s the Commutative Property.

2. 8 + (-8) = 0
→ Adding a number and its negative (opposite) gives zero. That’s the Inverse Property.

3. 4 + 0 = 4
→ Adding zero doesn’t change the number. That’s the Identity Property.

4. (9 + 3) + 6 = 9 + (3 + 6)
→ The grouping changes, but the result stays the same. That’s the Associative Property.

✔ So 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.

We need to compute the answer AND name which property is being used.

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

2. 3 + 12 = ?
→ Answer: 15
→ Property: Commutative Property? Wait — actually, this is just basic addition. But since no special rule is shown here (like swapping or grouping), it’s really just computation. However, looking at the context, maybe they want us to recognize if any property applies. Since 3 + 12 = 12 + 3, we could say Commutative — but the problem doesn’t show both orders. Actually, in this case, there’s no explicit property being demonstrated unless we assume commutativity. But let’s look again.

Wait — perhaps for #2, since it’s just straightforward addition with no trick, maybe they expect “None” or just the answer? But the instruction says “write the answers AND the addition properties”.

Looking back at the examples in Part A, every equation demonstrates one of the four properties.

So for #2: 3 + 12 = 15 — this doesn’t demonstrate identity, inverse, associative, or commutative explicitly... unless we consider that addition always allows commutativity, but the equation alone doesn’t show it.

Actually, let’s think differently. Maybe for problems like #2 and #4, where it’s just simple addition without zeros or negatives or parentheses, they still want us to note that it follows the general rules — but strictly speaking, only when the property is *demonstrated* should we name it.

But wait — look at #6: (15 + 2) + 1 — that clearly uses Associative Property because you can regroup as 15 + (2 + 1).

Similarly, #5: 10 + (-10) = 0 → Inverse Property.

#3: 0 + 13 = 13 → Identity Property (same as 13 + 0 = 13)

#1: 9 + 0 = 9 → Identity

#4: 18 + 3 = 21 → Again, just basic addition. But notice: 18 + 3 = 3 + 18 → so technically, it obeys Commutative Property, even though not written that way.

I think the intent is:

- If the equation involves adding zero → Identity
- If it involves adding a number and its opposite → Inverse
- If it shows regrouping → Associative
- If it shows swapped order → Commutative
- For plain addition like 3+12, since it’s equal to 12+3, we can say Commutative Property applies.

But to be precise, let’s match based on what’s visibly happening.

Re-evaluating:

1. 9 + 0 = 9 → Adding zero → Identity Property

2. 3 + 12 = 15 → No special feature, but since addition is commutative, and no other property fits, perhaps they expect Commutative Property? Or maybe just leave it as is? Hmm.

Wait — look at the worksheet design. In Part A, all examples clearly illustrate one of the four properties. In Part B, some do too:

- #1: 9 + 0 → Identity
- #3: 0 + 13 → also Identity (same thing)
- #5: 10 + (-10) → Inverse
- #6: (15 + 2) + 1 → Associative (because you can group differently)

For #2 and #4: 3 + 12 and 18 + 3 — these are just regular sums. But note: 3 + 12 = 12 + 3, so it illustrates Commutative Property implicitly. Similarly, 18 + 3 = 3 + 18.

In many curricula, even if not written out, such expressions are considered to follow the Commutative Property.

Alternatively, maybe for those two, since no property is visually demonstrated beyond basic arithmetic, but the question asks to “write the addition properties”, implying each has one.

Another angle: perhaps for #2 and #4, since they don’t involve zero, negatives, or parentheses, they might not have a specific property named — but that seems unlikely given the structure.

Let me check standard teaching materials. Usually, when students see “a + b = c” without any transformation, they aren’t expected to assign a property unless it’s illustrating one.

But looking at the worksheet again — in Part B, item #6 is clearly Associative. Item #5 is Inverse. Items #1 and #3 are Identity. That leaves #2 and #4.

Perhaps #2 and #4 are meant to be solved numerically, and the property is "none" or "basic addition", but that contradicts the pattern.

Wait — another idea: maybe for #2: 3 + 12 = 15, and since 3 and 12 are positive integers, and no special rule, but the act of adding them relies on the closure property or something — but that’s not listed.

The table only lists four properties: Commutative, Associative, Identity, Inverse.

So for 3 + 12 = 15, none of those are directly illustrated — unless we say it satisfies Commutative because 3+12=12+3.

I think the safest approach is:

- When the expression matches the form of one of the properties exactly, use that.
- Otherwise, if it’s just a sum, and no property is shown, perhaps skip naming — but the instruction says “write the answers and the addition properties”.

Looking at similar worksheets online, often for simple additions like 5 + 7, they still say “Commutative Property” because it’s understood that order doesn’t matter.

To resolve this, let’s assume:

- Any addition of two numbers without zero/negative/parentheses → Commutative Property (since it implies a + b = b + a)

That makes sense pedagogically.

So:

2. 3 + 12 = 15 → Commutative Property
4. 18 + 3 = 21 → Commutative Property

Yes, that works.

And for #6: (15 + 2) + 1 = 18, and it demonstrates Associative Property because you can write it as 15 + (2 + 1) = 15 + 3 = 18.

Final verification:

B1: 9 + 0 = 9 → Identity
B2: 3 + 12 = 15 → Commutative
B3: 0 + 13 = 13 → Identity
B4: 18 + 3 = 21 → Commutative
B5: 10 + (-10) = 0 → Inverse
B6: (15 + 2) + 1 = 18 → Associative

All covered!

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Final Answer:

A)
① Commutative Property
② Inverse Property
③ Identity Property
④ Associative Property

B)
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