Math worksheet from Math Monks focusing on the properties of addition, including identification and application exercises.

Let’s go through each part of the worksheet step by step.

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Part A: Identify the property of additions for each.

We have four properties defined at the top:

- Commutative Property: Order doesn’t matter → a + b = b + a
- Associative Property: Grouping doesn’t matter → (a + b) + c = a + (b + c)
- Identity Property: Adding zero gives the same number → a + 0 = a
- Inverse Property: A number plus its negative equals zero → a + (-a) = 0

Now let’s match each problem:

① 7 + 3 = 3 + 7
→ The order changed, but sum is same → This is Commutative Property

② 8 + (-8) = 0
→ A number added to its opposite gives zero → This is Inverse Property

③ 4 + 0 = 4
→ Adding zero didn’t change the number → This is Identity Property

④ (9 + 3) + 6 = 9 + (3 + 6)
→ The grouping changed, but result is same → This is Associative Property

✔ All matched correctly.

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

We’ll compute each answer and 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 regular addition. But since no special rule is being demonstrated here (like changing order or grouping), we can say it’s basic addition. However, looking at context, maybe they want us to note if any property applies. Since 3 + 12 = 12 + 3, it *could* be commutative, but the problem doesn’t show that. Actually, in this case, there’s no trick — it’s straightforward. But perhaps the worksheet expects us to identify which property is illustrated — and none really are except maybe identity or inverse elsewhere. Let’s check all.

Actually, rethinking: In Part B, some problems illustrate specific properties. Let’s analyze each:

① 9 + 0 = 9 → Identity Property
② 3 + 12 = 15 → No special property shown; just standard addition. But wait — maybe they expect “Commutative” because you could write 12 + 3? But the problem doesn’t do that. Hmm. Looking back at Part A, they gave equations that clearly show the property. Here, only some will show a property.

Let’s look again:

③ 0 + 13 = 13 → Again, adding zero → Identity Property
④ 18 + 3 = 21 → Just normal addition. Could be commutative if written as 3 + 18, but not shown. So probably just state answer.
⑤ 10 + (-10) = 0 → Inverse Property
⑥ (15 + 2) + 1 = 18 → Associative Property? Let’s see: (15+2)+1 = 17+1=18, and 15+(2+1)=15+3=18 → yes, associative. But the equation isn’t rewritten with different grouping — so maybe they just want the answer? Wait, the instruction says: “Write the answers and the addition properties”

So for each, we must give both the numerical answer AND the property involved.

Let’s go one by one carefully:

① 9 + 0 = 9 → Property: Identity Property
② 3 + 12 = 15 → What property? It’s not identity, inverse, or associative. It *is* commutative in nature (since 3+12=12+3), but the expression doesn’t show switching. However, in many worksheets like this, even simple sums without zero or negatives are considered under Commutative if implied. But strictly speaking, this problem alone doesn’t demonstrate a property unless compared to 12+3. Maybe the worksheet intends for us to recognize that all addition follows these rules, but only some explicitly show them.

Wait — looking at Part A, they had clear examples. In Part B, perhaps only those that involve 0, negatives, or parentheses are meant to highlight a property. For others, maybe we just write the answer and say “basic addition” or leave property blank? But the instruction says “write the answers and the addition properties”.

Alternatively, perhaps for #2 and #4, since they don’t involve 0, -a, or grouping, they might not require a named property — but that seems odd.

Another thought: Maybe for #2 and #4, they are testing whether students know that commutative property allows rearranging, but since it’s not shown, perhaps we should still assign "Commutative" as the underlying principle? That feels forced.

Let me check online or common practice: In such worksheets, when an equation like “3 + 12 =” is given without comparison, and asked for property, sometimes they expect “None” or “Basic Addition”, but more often, if it’s standalone, they may not assign a property unless it demonstrates one.

But looking at the structure: Part A was identifying from equations that clearly show the property. Part B is computing and stating the property — implying that each does illustrate one.

Let’s list them with reasoning:

① 9 + 0 = 9 → Identity (clear)
② 3 + 12 = 15 → If we think about it, 3 + 12 is the same as 12 + 3, so it illustrates Commutative Property — even though not written, the fact that we’re adding two numbers implies commutativity holds. Many teachers accept this.
③ 0 + 13 = 13 → Identity (same as #1)
④ 18 + 3 = 21 → Similarly, 18 + 3 = 3 + 18 → Commutative
⑤ 10 + (-10) = 0 → Inverse (clear)
⑥ (15 + 2) + 1 = 18 → This shows grouping: first add 15+2, then +1. We could also do 15 + (2+1) = 15+3=18 → so Associative Property. Even though not rewritten, the presence of parentheses suggests associativity is being tested.

Yes, that makes sense. So:

① Answer: 9, Property: Identity
② Answer: 15, Property: Commutative
③ Answer: 13, Property: Identity
④ Answer: 21, Property: Commutative
⑤ Answer: 0, Property: Inverse
⑥ Answer: 18, Property: Associative

Double-check calculations:

① 9 + 0 = 9 ✓
② 3 + 12 = 15 ✓
③ 0 + 13 = 13 ✓
④ 18 + 3 = 21 ✓
⑤ 10 + (-10) = 0 ✓
⑥ (15 + 2) + 1 = 17 + 1 = 18 ✓

All correct.

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Final Answers Compiled:

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

B)
① 9, Identity Property
② 15, Commutative Property
③ 13, Identity Property
④ 21, Commutative Property
⑤ 0, Inverse Property
⑥ 18, Associative Property

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Final Answer:
A) ① Commutative Property, ② Inverse Property, ③ Identity Property, ④ Associative Property
B) ① 9, Identity Property; ② 15, Commutative Property; ③ 13, Identity Property; ④ 21, Commutative Property; ⑤ 0, Inverse Property; ⑥ 18, Associative Property