Properties of Addition Worksheets with Answer Key - Free Printable

Let's solve each part of the worksheet step by step and explain the reasoning.

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

#### 1) $ 9 + 3 = 3 + \_\_\_\_ $

- We are swapping the order of 9 and 3.
- This is the Commutative Property: $ a + b = b + a $
- So, $ 9 + 3 = 3 + 9 $

✔ Answer: $ 9 $, Property: Commutative Property

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#### 2) $ 3 + (4 + 6) = (3 + \_\_\_\_) + 6 $

- The grouping changes: from $ 3 + (4 + 6) $ to $ (3 + \_\_) + 6 $
- We're changing how the numbers are grouped, but not their order.
- This is the Associative Property: $ a + (b + c) = (a + b) + c $
- So, $ 3 + (4 + 6) = (3 + 4) + 6 $

✔ Answer: $ 4 $, Property: Associative Property

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#### 3) $ 39 + 0 = \_\_\_\_\_\_\_\_ $

- Adding zero to any number gives the same number.
- This is the Identity Property: $ a + 0 = a $
- So, $ 39 + 0 = 39 $

✔ Answer: $ 39 $, Property: Identity Property

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#### 4) $ (30 + 1) + 6 = \_\_\_\_ + (1 + 6) $

- Let's look at both sides:
- Left: $ (30 + 1) + 6 = 31 + 6 $
- Right: $ \_\_ + (1 + 6) = \_\_ + 7 $
- For this to be true: $ 31 + 6 = 37 $, so right side must also be 37 → $ \_\_ + 7 = 37 $ → $ \_\_ = 30 $
- But more importantly, we are reordering and regrouping.
- The original expression is $ (30 + 1) + 6 $
- We want to write it as $ \_\_ + (1 + 6) $
- That means we’re moving 30 outside the group with 1 and 6.
- This uses Associative Property and possibly Commutative, but here the key is that we're regrouping.
- Actually, $ (30 + 1) + 6 = 30 + (1 + 6) $ — yes! This is Associative Property
- So the missing number is 30

✔ Answer: $ 30 $, Property: Associative Property

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B) Write each equation using commutative property.

> The Commutative Property says: $ a + b = b + a $

#### 1) $ 3 + 20 = 23 $

- Swap the addends: $ 20 + 3 = 23 $

✔ Answer: $ 20 + 3 = 23 $

#### 2) $ 12 + 13 = 25 $

- Swap the addends: $ 13 + 12 = 25 $

✔ Answer: $ 13 + 12 = 25 $

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C) Write each equation using associative property.

> The Associative Property says: $ a + (b + c) = (a + b) + c $

#### 1) $ (3 + 15) + 6 = 24 $

- Change grouping: move parentheses from $ (3 + 15) + 6 $ to $ 3 + (15 + 6) $
- $ 3 + (15 + 6) = 3 + 21 = 24 $ → still valid

✔ Answer: $ 3 + (15 + 6) = 24 $

#### 2) $ 9 + (5 + 6) = 20 $

- Change grouping: $ (9 + 5) + 6 = 20 $
- $ 9 + 5 = 14 $, $ 14 + 6 = 20 $ → correct

✔ Answer: $ (9 + 5) + 6 = 20 $

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D) Which of the following represents the inverse property?

> The Inverse Property of addition: $ a + (-a) = 0 $

Let’s check each option:

#### 1) $ 18 + 2 = 2 + 18 $

- This is commutative property → ✘

#### 2) $ 2 + (13 + 3) = 18 $

- Just an addition equation; no negative number involved → ✘

#### 3) $ 19 + (-19) = 0 $

- Yes! $ a + (-a) = 0 $ → This is the Inverse Property ✔

#### 4) $ 30 + 0 = 30 $

- This is the Identity Property → ✘

✔ Answer: Option 3

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✔ Final Answers Summary:

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A)
1) $ 9 $, Commutative Property
2) $ 4 $, Associative Property
3) $ 39 $, Identity Property
4) $ 30 $, Associative Property

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B)
1) $ 20 + 3 = 23 $
2) $ 13 + 12 = 25 $

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

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D)
✔ Option 3: $ 19 + (-19) = 0 $

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