Properties of Addition Worksheets with Answer Key - Free Printable

Let’s solve each part step by step, using the Addition Properties table provided:

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A) Find the missing numbers. Also identify the property.

#### ① 9 + 3 = 3 + ___
→ This is commutative property: order doesn’t matter → `a + b = b + a`
So, 9 + 3 = 3 + 9
✔ Answer: 9 — Commutative Property

#### ② 3 + (4 + 6) = (3 + ___) + 6
→ This is associative property: grouping doesn’t matter → `a + (b + c) = (a + b) + c`
So, 3 + (4 + 6) = (3 + 4) + 6
✔ Answer: 4 — Associative Property

#### ③ 39 + 0 = ___
→ This is identity property: adding zero doesn’t change the number → `a + 0 = a`
So, 39 + 0 = 39
✔ Answer: 39 — Identity Property

#### ④ (30 + 1) + 6 = ___ + (1 + 6)
→ Again, associative property: regrouping → `(a + b) + c = a + (b + c)`
So, (30 + 1) + 6 = 30 + (1 + 6)
✔ Answer: 30 — Associative Property

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B) Write each equation using commutative property.

Commutative property means switch the order of the addends.

#### ① 3 + 20 = 23
→ Switch 3 and 20: 20 + 3 = 23
✔ Answer: 20 + 3 = 23

#### ② 12 + 13 = 25
→ Switch 12 and 13: 13 + 12 = 25
✔ Answer: 13 + 12 = 25

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C) Write each equation using associative property.

Associative property means regroup the numbers — change which two you add first.

#### ① (3 + 15) + 6 = 24
→ Regroup: 3 + (15 + 6) = 24
✔ Answer: 3 + (15 + 6) = 24

#### ② 9 + (5 + 6) = 20
→ Regroup: (9 + 5) + 6 = 20
✔ Answer: (9 + 5) + 6 = 20

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D) Which of the following represents the inverse property?

Inverse property: `a + (-a) = 0` → a number plus its opposite equals zero.

Check each option:

#### ① 18 + 2 = 2 + 18 → Commutative → ✘
#### ② 2 + (13 + 3) = 18 → Associative (but not showing inverse) → ✘
#### ③ 19 + (-19) = 0 → YES! This matches `a + (-a) = 0` → ✔
#### ④ 30 + 0 = 30 → Identity → ✘

✔ Answer: ③ 19 + (-19) = 0

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## ✔ Final Answers Summary:

A)

1. 9 — Commutative Property
2. 4 — Associative Property
3. 39 — Identity Property
4. 30 — Associative Property

B)

1. 20 + 3 = 23
2. 13 + 12 = 25

C)

1. 3 + (15 + 6) = 24
2. (9 + 5) + 6 = 20

D)

③ 19 + (-19) = 0

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