Properties of Numbers interactive worksheet - Free Printable

To solve the problem, we need to identify which property of numbers each equation demonstrates. The properties are:

1. Distributive Property: \( a \times (b + c) = (a \times b) + (a \times c) \)
2. Commutative Property: \( a + b = b + a \) or \( a \times b = b \times a \)
3. Associative Property: \( (a + b) + c = a + (b + c) \) or \( (a \times b) \times c = a \times (b \times c) \)
4. Identity Property: \( a + 0 = a \) or \( a \times 1 = a \)

Let's analyze each equation step by step:

---

1. \( 5 + 2 = 2 + 5 \)

- This shows that the order of addition does not matter.
- Property: Commutative

---

2. \( 2 \times 8 = 8 \times 2 \)

- This shows that the order of multiplication does not matter.
- Property: Commutative

---

3. \( 13 \times 2 = 2 \times 13 \)

- This shows that the order of multiplication does not matter.
- Property: Commutative

---

4. \( 8 \times 1 = 8 \)

- Multiplying any number by 1 gives the same number.
- Property: Identity

---

5. \( 1 \times 6 = 6 \)

- Multiplying any number by 1 gives the same number.
- Property: Identity

---

6. \( 12 \times (3 \times 4) = (12 \times 3) \times 4 \)

- This shows that the grouping of factors does not affect the product.
- Property: Associative

---

7. \( 8 \times (2 \times 4) = (8 \times 2) \times 4 \)

- This shows that the grouping of factors does not affect the product.
- Property: Associative

---

8. \( (2 \times 4) + (2 \times 3) = 2 \times (4 + 3) \)

- This shows the distributive property: multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
- Property: Distributive

---

9. \( (12 \times 8) + (12 \times 1) = 12 \times (8 + 1) \)

- This shows the distributive property: multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
- Property: Distributive

---

10. \( 6 \times 7 = 7 \times 6 \)

- This shows that the order of multiplication does not matter.
- Property: Commutative

---

11. \( (7 \times 5) - (7 \times 4) = 7 \times (5 - 4) \)

- This shows the distributive property: subtracting products is the same as multiplying the number by the difference of the factors.
- Property: Distributive

---

12. \( 5 \times (4 \times 9) = (5 \times 4) \times 9 \)

- This shows that the grouping of factors does not affect the product.
- Property: Associative

---

13. \( 7 \times (15 \times 10) = (7 \times 15) \times 10 \)

- This shows that the grouping of factors does not affect the product.
- Property: Associative

---

14. \( 2 \times (13 \times 14) = (2 \times 13) \times 14 \)

- This shows that the grouping of factors does not affect the product.
- Property: Associative

---

15. \( 1 \times 64 = 64 \)

- Multiplying any number by 1 gives the same number.
- Property: Identity

---

16. \( 18 \times (2 + 9) = (18 \times 2) + (18 \times 9) \)

- This shows the distributive property: multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
- Property: Distributive

---

17. \( 0 \times 8 = 8 \times 0 \)

- Multiplying any number by 0 gives 0.
- Property: Identity (specifically, the multiplicative identity property with 0)

---

18. \( 4 \times (10 + 6) = (4 \times 10) + (4 \times 6) \)

- This shows the distributive property: multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.
- Property: Distributive

---

19. \( 0 + 5 = 5 \)

- Adding 0 to any number gives the same number.
- Property: Identity

---

20. \( 11 \times 1 = 11 \)

- Multiplying any number by 1 gives the same number.
- Property: Identity

---

Final Answer

Here is the completed table:

| Number | Equation | Property |
|--------|------------------------------------|----------------|
| 1 | \( 5 + 2 = 2 + 5 \) | Commutative |
| 2 | \( 2 \times 8 = 8 \times 2 \) | Commutative |
| 3 | \( 13 \times 2 = 2 \times 13 \) | Commutative |
| 4 | \( 8 \times 1 = 8 \) | Identity |
| 5 | \( 1 \times 6 = 6 \) | Identity |
| 6 | \( 12 \times (3 \times 4) = (12 \times 3) \times 4 \) | Associative |
| 7 | \( 8 \times (2 \times 4) = (8 \times 2) \times 4 \) | Associative |
| 8 | \( (2 \times 4) + (2 \times 3) = 2 \times (4 + 3) \) | Distributive |
| 9 | \( (12 \times 8) + (12 \times 1) = 12 \times (8 + 1) \) | Distributive |
| 10 | \( 6 \times 7 = 7 \times 6 \) | Commutative |
| 11 | \( (7 \times 5) - (7 \times 4) = 7 \times (5 - 4) \) | Distributive |
| 12 | \( 5 \times (4 \times 9) = (5 \times 4) \times 9 \) | Associative |
| 13 | \( 7 \times (15 \times 10) = (7 \times 15) \times 10 \) | Associative |
| 14 | \( 2 \times (13 \times 14) = (2 \times 13) \times 14 \) | Associative |
| 15 | \( 1 \times 64 = 64 \) | Identity |
| 16 | \( 18 \times (2 + 9) = (18 \times 2) + (18 \times 9) \) | Distributive |
| 17 | \( 0 \times 8 = 8 \times 0 \) | Identity |
| 18 | \( 4 \times (10 + 6) = (4 \times 10) + (4 \times 6) \) | Distributive |
| 19 | \( 0 + 5 = 5 \) | Identity |
| 20 | \( 11 \times 1 = 11 \) | Identity |

Boxed Answer:
\[
\boxed{
\begin{array}{c|c}
\text{Number} & \text{Property} \\
\hline
1 & \text{Commutative} \\
2 & \text{Commutative} \\
3 & \text{Commutative} \\
4 & \text{Identity} \\
5 & \text{Identity} \\
6 & \text{Associative} \\
7 & \text{Associative} \\
8 & \text{Distributive} \\
9 & \text{Distributive} \\
10 & \text{Commutative} \\
11 & \text{Distributive} \\
12 & \text{Associative} \\
13 & \text{Associative} \\
14 & \text{Associative} \\
15 & \text{Identity} \\
16 & \text{Distributive} \\
17 & \text{Identity} \\
18 & \text{Distributive} \\
19 & \text{Identity} \\
20 & \text{Identity} \\
\end{array}
}
\]