Addition Properties Worksheet - Free Printable

Let's solve the worksheet step by step and explain each answer.

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Part 1: Choose the correct addition property

We are given pairs of equations and asked to identify which addition property is being shown. 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 is switched, but the sum remains the same.
- This shows the commutative property.

✔ 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 → identity property.

✔ Answer: (b) identity

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#### 4)
$$
(5 + 4) + 3 = 12 \\
5 + (4 + 3) = 12
$$
- The grouping changes: first (5+4), then (4+3), but the sum is the same.
- This shows the associative property.

✔ Answer: (a) associative

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#### 5)
$$
6 + 9 = 15 \\
9 + 6 = 15
$$
- Order of numbers is switched → commutative property.

✔ Answer: (c) commutative

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Part 2: Solve the following

#### 6)
$$
13 + 14 = \boxed{27} \\
14 + 13 = \boxed{27}
$$
- Both sums are equal due to the commutative property.

✔ Answers: 27, 27

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#### 7)
$$
20 + 0 = \boxed{20}
$$
- Identity property: any number plus zero is itself.

✔ Answer: 20

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#### 8)
$$
(10 + 4) + 8 = 14 + 8 = \boxed{22} \\
10 + (4 + 8) = 10 + 12 = \boxed{22}
$$
- Same sum regardless of grouping → associative property.

✔ Answers: 22, 22

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Review: Multiplication Problems

Now, solve the multiplication facts:

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

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✔ Final Answers:

#### Multiple Choice (1–5):
1. (c) commutative
2. (b) identity
3. (b) identity
4. (a) associative
5. (c) commutative

#### Solve (6–8):
6. 13 + 14 = 27, 14 + 13 = 27
7. 20 + 0 = 20
8. (10 + 4) + 8 = 22, 10 + (4 + 8) = 22

#### Review (Multiplication):
- 8 × 6 = 48
- 8 × 4 = 32
- 8 × 12 = 96
- 6 × 7 = 42
- 5 × 4 = 20
- 7 × 9 = 63

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