Properties of addition worksheet grade 4 - Free Printable

Let's solve the problem step by step based on the worksheet titled "Identity and Commutative Property of Addition."

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Part 1: Identify whether each number sentence is the Identity or Commutative property.

#### Definitions:
- Identity Property of Addition:
Adding zero to any number does not change the value.
Example: $ a + 0 = a $

- Commutative Property of Addition:
The order of addends does not affect the sum.
Example: $ a + b = b + a $

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Now, let’s analyze each statement:

1. 7+0 = 7
→ Adding zero to 7. This is the Identity Property.

2. 50+3 = 3+50
→ Order changed. This is the Commutative Property.

3. 307 + 0 = 307
→ Adding zero. This is the Identity Property.

4. 0+6 = 6
→ Adding zero. This is the Identity Property.

5. 1+2 = 2+1
→ Order changed. This is the Commutative Property.

6. 8+0 = 8
→ Adding zero. This is the Identity Property.

7. 4+9 = 9+4
→ Order changed. This is the Commutative Property.

8. 14+2 = 9+14
→ Let's check:
Left side: $ 14 + 2 = 16 $
Right side: $ 9 + 14 = 23 $
$ 16 \neq 23 $ → This is not true, so it's neither identity nor commutative.
But since the question asks to identify if it's one of the two properties, and it's false, we can say: Neither (or possibly a mistake in the problem).

However, note: the equation is not true, so it doesn't represent either property correctly.

9. 1+0 = 0
→ $ 1 + 0 = 1 $, but here it says $ = 0 $. This is false.
So, this is not an example of identity property. It's incorrect.

10. 0+4 = 4
→ Adding zero. This is the Identity Property.

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✔ Part 1 Answers:

| Number | Statement | Property |
|--------|-------------------------|--------------------------|
| 1 | 7+0 = 7 | Identity |
| 2 | 50+3 = 3+50 | Commutative |
| 3 | 307 + 0 = 307 | Identity |
| 4 | 0+6 = 6 | Identity |
| 5 | 1+2 = 2+1 | Commutative |
| 6 | 8+0 = 8 | Identity |
| 7 | 4+9 = 9+4 | Commutative |
| 8 | 14+2 = 9+14 | Neither (False) |
| 9 | 1+0 = 0 | Neither (False) |
| 10 | 0+4 = 4 | Identity |

> Note: #8 and #9 are incorrect equations, so they don’t demonstrate either property properly.

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Part 2: Fill in the blank with the correct number to make the sentence true.

11. 5+ ____ = 7+5
→ We want the left side to equal the right side.
Right side: $ 7 + 5 = 12 $
So: $ 5 + x = 12 $ → $ x = 7 $
✔ Answer: 7

12. ____ + 2 = 2
→ $ x + 2 = 2 $ → $ x = 0 $
✔ Answer: 0

13. 19 + ____ = 19
→ To keep the same value, we add zero.
✔ Answer: 0

14. 13 + ____ = 13
→ Same as above. Add zero.
✔ Answer: 0

15. 34 + 0 = ____
→ $ 34 + 0 = 34 $
✔ Answer: 34

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✔ Part 2 Answers:

11. 7
12. 0
13. 0
14. 0
15. 34

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✔ Final Answer Summary:

#### Part 1: Identify the Property
1. Identity
2. Commutative
3. Identity
4. Identity
5. Commutative
6. Identity
7. Commutative
8. Neither (False)
9. Neither (False)
10. Identity

#### Part 2: Fill in the Blank
11. 7
12. 0
13. 0
14. 0
15. 34

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