Question: Write down all of the following that use commutative laws.
3 × 5 = 5 × 3
(2 + 4) + 7 = 2 + (4 + 7)
8 + 9 = 9 + 8
6 × (7 - 3) = 6 × 7 - 6 × 3
(3 × 2) × 6 = 3 × (2 × 6)
5 × (2 + 8) = 5 × 2 + 5 × 8
1. **State the problem:** Identify which of the given equations use the commutative law.
2. **Recall the commutative laws:**
- Commutative law of addition: $$a + b = b + a$$
- Commutative law of multiplication: $$a \times b = b \times a$$
3. **Analyze each equation:**
- $$3 \times 5 = 5 \times 3$$ uses multiplication and swaps the factors, so it uses the commutative law of multiplication.
- $$(2 + 4) + 7 = 2 + (4 + 7)$$ is an example of the associative law of addition, not commutative.
- $$8 + 9 = 9 + 8$$ uses addition and swaps the addends, so it uses the commutative law of addition.
- $$6 \times (7 - 3) = 6 \times 7 - 6 \times 3$$ is the distributive law, not commutative.
- $$(3 \times 2) \times 6 = 3 \times (2 \times 6)$$ is the associative law of multiplication, not commutative.
- $$5 \times (2 + 8) = 5 \times 2 + 5 \times 8$$ is the distributive law, not commutative.
4. **Final answer:** The equations that use the commutative law are:
$$3 \times 5 = 5 \times 3$$
$$8 + 9 = 9 + 8$$