Addition Properties exercise - Free Printable

Let's solve the problem step by step.

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Part 1: Choose the correct addition property (Questions 1–5)

We need to identify which addition property is demonstrated in each case. The three properties are:

- Commutative Property: Changing the order of numbers does not change the sum.
Example: $ a + b = b + a $

- Associative Property: Changing the grouping of numbers does not change the sum.
Example: $ (a + b) + c = a + (b + c) $

- Identity Property: Adding zero to a number does not change its value.
Example: $ a + 0 = a $

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#### 1)
$$
4 + 9 = 13 \\
9 + 4 = 13
$$
→ The order of the numbers changed, but the sum stayed the same.

✔ Answer: (c) commutative

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#### 2)
$$
5 + 0 = 5
$$
→ Adding zero to 5 gives 5. This is the identity property.

✔ Answer: (b) identity

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#### 3)
$$
10 + 0 = 10
$$
→ Again, adding zero doesn’t change the number.

✔ Answer: (b) identity

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#### 4)
$$
(5 + 4) + 3 = 12 \\
5 + (4 + 3) = 12
$$
→ The grouping changed: first (5+4), then (4+3), but the sum is the same.

✔ Answer: (a) associative

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#### 5)
$$
6 + 9 = 15 \\
9 + 6 = 15
$$
→ Order changed, sum remains same.

✔ Answer: (c) commutative

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✔ Answers for Questions 1–5:

1. (c) commutative
2. (b) identity
3. (b) identity
4. (a) associative
5. (c) commutative

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Part 2: Solve the following

#### 6) $ 13 + 14 = \ ? $ and $ 14 + 13 = \ ? $

- $ 13 + 14 = 27 $
- $ 14 + 13 = 27 $

✔ Answers: 27, 27

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#### 7) $ 20 + 0 = \ ? $

→ Identity property: adding zero doesn’t change the number.

✔ Answer: 20

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#### 8) $ (10 + 4) + 8 = \ ? $ and $ 10 + (4 + 8) = \ ? $

- $ (10 + 4) + 8 = 14 + 8 = 22 $
- $ 10 + (4 + 8) = 10 + 12 = 22 $

✔ Answers: 22, 22

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Review: Multiplication Problems

Now solve the multiplication facts:

- $ 8 \times 6 = 48 $
- $ 8 \times 4 = 32 $
- $ 8 \times 12 = 96 $
- $ 6 \times 7 = 42 $
- $ 5 \times 4 = 20 $
- $ 7 \times 9 = 63 $

✔ Review Answers:
- 48, 32, 96
- 42, 20, 63

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✔ Final Answer Summary:

#### Addition Properties:
1. (c) commutative
2. (b) identity
3. (b) identity
4. (a) associative
5. (c) commutative

#### Solve:
6) 27, 27
7) 20
8) 22, 22

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

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