Properties of Addition Worksheets with Answer Key - Free Printable

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 (since 3 + 12 = 12 + 3, but the question just asks for answer and property; no rearrangement shown, so only answer needed—property not required unless specified; but based on instructions, we give answer and property if asked. Since B says “Write the answers and the addition properties”, we include both.)
Actually, re-reading B: “Write the answers and the addition properties for the following”—so each needs answer + property.

Let’s do each carefully:

① 9 + 0 = 9 → Identity Property
② 3 + 12 = 15 → Commutative Property (because addition is commutative, though not shown rearranged; but since no grouping or zero/negative, the underlying property that allows us to compute it freely is commutativity—but strictly, just computing doesn’t *use* a property unless structure matches. However, in this context, they likely expect: if it’s just two numbers added, and no special form, maybe no property is *illustrated*, but the worksheet expects matching to one of the four. Let’s check patterns:

- Only when 0 is involved → Identity
- When a + (–a) → Inverse
- When order swapped (a+b = b+a) → Commutative
- When parentheses regrouped → Associative

So:
① 9 + 0 = 9 → Identity
② 3 + 12 = 15 → No special property shown; but since it's just two positives, and no rearrangement, technically none of the four are *demonstrated*. However, in many curricula, they still say “Commutative Property applies” because addition of two numbers always satisfies commutativity—even if not written both ways. But the instruction says “identify the property *for each*” in A, and in B “write the answers and the addition properties”, implying each has one.

Looking at B examples:
③ 0 + 13 = 13 → Identity
④ 18 + 3 = 21 → Commutative (since 18+3 = 3+18, though not written)
⑤ 10 + (–10) = 0 → Inverse
⑥ (15 + 2) + 1 = 18 → Associative (because (15+2)+1 = 15+(2+1), and result is same)

So we assign:

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

But the final answer should be concise as per format: only the final correct answer, no explanations (since ExplainAnswer = false).

So list all answers clearly:

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

Now format as single final answer block:

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