Addition Properties Worksheet for Math Practice

Problem Analysis:

The worksheet focuses on addition properties and basic arithmetic operations. Let's break it down step by step:

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#### Part 1: Addition Properties (Questions 1-5)

We need to identify which addition property is being demonstrated in each equation. The three properties are:
1. Commutative Property: $ a + b = b + a $ (order of addition does not matter).
2. Identity Property: $ a + 0 = a $ (adding zero does not change the number).
3. Associative Property: $ (a + b) + c = a + (b + c) $ (grouping of numbers does not matter).

##### Question 1:
$$
4 + 9 = 13 \quad \text{and} \quad 9 + 4 = 13
$$
- This shows that changing the order of the numbers does not affect the sum.
- Property: Commutative.

##### Question 2:
$$
5 + 0 = 5
$$
- Adding zero to a number leaves the number unchanged.
- Property: Identity.

##### Question 3:
$$
10 + 0 = 10
$$
- Adding zero to a number leaves the number unchanged.
- Property: Identity.

##### Question 4:
$$
(5 + 4) + 3 = 12 \quad \text{and} \quad 5 + (4 + 3) = 12
$$
- This shows that the grouping of numbers does not affect the sum.
- Property: Associative.

##### Question 5:
$$
6 + 9 = 15 \quad \text{and} \quad 9 + 6 = 15
$$
- This shows that changing the order of the numbers does not affect the sum.
- Property: Commutative.

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#### Part 2: Solve the Following (Questions 6-8)

##### Question 6:
$$
13 + 14 = \_\_\_\_ \quad \text{and} \quad 14 + 13 = \_\_\_\_
$$
- Using the commutative property, the order of addition does not matter.
- Calculate: $ 13 + 14 = 27 $.
- Therefore: $ 14 + 13 = 27 $ as well.

##### Question 7:
$$
20 + 0 = \_\_\_\_
$$
- Using the identity property, adding zero does not change the number.
- Therefore: $ 20 + 0 = 20 $.

##### Question 8:
$$
(10 + 4) + 8 = \_\_\_\_ \quad \text{and} \quad 10 + (4 + 8) = \_\_\_\_
$$
- Using the associative property, the grouping of numbers does not matter.
- First, calculate $ 10 + 4 = 14 $, then $ 14 + 8 = 22 $.
- Alternatively, calculate $ 4 + 8 = 12 $, then $ 10 + 12 = 22 $.
- Therefore: $ (10 + 4) + 8 = 22 $ and $ 10 + (4 + 8) = 22 $.

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#### Part 3: Review (Multiplication Problems)

These are straightforward multiplication problems.

##### Question 8:
$$
8 \times 6 = \_\_\_\_, \quad 8 \times 4 = \_\_\_\_, \quad 8 \times 12 = \_\_\_\_
$$
- Calculate each:
- $ 8 \times 6 = 48 $
- $ 8 \times 4 = 32 $
- $ 8 \times 12 = 96 $

##### Question 9:
$$
6 \times 7 = \_\_\_\_, \quad 5 \times 4 = \_\_\_\_, \quad 7 \times 9 = \_\_\_\_
$$
- Calculate each:
- $ 6 \times 7 = 42 $
- $ 5 \times 4 = 20 $
- $ 7 \times 9 = 63 $

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Final Answers:

1. Commutative
2. Identity
3. Identity
4. Associative
5. Commutative

6. $ 13 + 14 = 27 $, $ 14 + 13 = 27 $
7. $ 20 + 0 = 20 $
8. $ (10 + 4) + 8 = 22 $, $ 10 + (4 + 8) = 22 $

Review:
8. $ 8 \times 6 = 48 $, $ 8 \times 4 = 32 $, $ 8 \times 12 = 96 $
9. $ 6 \times 7 = 42 $, $ 5 \times 4 = 20 $, $ 7 \times 9 = 63 $

Boxed Final Answer:
$$
\boxed{
\text{1. (c), 2. (b), 3. (b), 4. (a), 5. (c), 6. 27, 27, 7. 20, 8. 22, 22, 9. 48, 32, 96, 42, 20, 63}
}
$$