Properties of Real Numbers Worksheets - 15 Worksheets Library - Free Printable

Sure! Let’s go through each exercise and identify the property of real numbers being used. I’ll explain each one clearly.

---

1. (a)(d) = (d)(a)

✔ Commutative Property of Multiplication
*Explanation:* The order of multiplication doesn’t matter: a × d = d × a.

---

2. (8 + 2) + 4 = 8 + (2 + 4)

✔ Associative Property of Addition
*Explanation:* Grouping doesn’t affect the sum: (a + b) + c = a + (b + c).

---

3. 8(1) = 8

✔ Multiplicative Identity Property
*Explanation:* Any number multiplied by 1 stays the same: a × 1 = a.

---

4. 42 – 6a = 6(7 – a)

✔ Distributive Property
*Explanation:* Distributing the 6 over the parentheses: 6 × 7 = 42, and 6 × (-a) = -6a. So, 6(7 – a) = 42 – 6a.

---

5. f + 0 = f

✔ Additive Identity Property
*Explanation:* Adding zero to any number leaves it unchanged: a + 0 = a.

---

6. –14 + 14 = 0

✔ Additive Inverse Property
*Explanation:* A number plus its opposite equals zero: a + (–a) = 0.

---

7. 3a + 2b = 2b + 3a

✔ Commutative Property of Addition
*Explanation:* Order of addition doesn’t matter: a + b = b + a.

---

8. 5(7c) = (5 × 7)c

✔ Associative Property of Multiplication
*Explanation:* Grouping doesn’t affect the product: a(bc) = (ab)c.

*(Note: Some might confuse this with distributive, but since there’s no addition inside the parentheses, it’s associative.)*

---

9. 36 + 48 = 48 + 14

⚠️ This is incorrect as written!
36 + 48 = 84, but 48 + 14 = 62 → Not equal!

But if we assume it’s a typo and meant to be 36 + 48 = 48 + 36, then:

✔ Commutative Property of Addition

*However, as written, it’s mathematically false. Since this is likely a worksheet error, we’ll assume the intended expression was 36 + 48 = 48 + 36.*

---

10. xy + 0 = xy

✔ Additive Identity Property
*Explanation:* Adding zero to any expression leaves it unchanged.

---

11. 99 + 0 = 99

✔ Additive Identity Property
*Explanation:* Same as #5 — adding zero does nothing.

---

12. 4 + 5 + 6 = 6 + 4 + 5

✔ Commutative Property of Addition
*Explanation:* The order of addends can be rearranged without changing the sum.

---

## ✔ Final Answer Table:

| N° | Exercise | Property |
|----|--------------------|------------------------------|
| 1 | (a)(d) = (d)(a) | Commutative Property of Multiplication |
| 2 | (8+2)+4 = 8+(2+4) | Associative Property of Addition |
| 3 | 8(1) = 8 | Multiplicative Identity Property |
| 4 | 42 – 6a = 6(7 – a) | Distributive Property |
| 5 | f + 0 = f | Additive Identity Property |
| 6 | –14 + 14 = 0 | Additive Inverse Property |
| 7 | 3a + 2b = 2b + 3a | Commutative Property of Addition |
| 8 | 5(7c) = (5×7)c | Associative Property of Multiplication |
| 9 | 36 + 48 = 48 + 14 | ✘ Incorrect — likely meant Commutative Property of Addition (if corrected to 36 + 48 = 48 + 36) |
|10 | xy + 0 = xy | Additive Identity Property |
|11 | 99 + 0 = 99 | Additive Identity Property |
|12 | 4 + 5 + 6 = 6 + 4 + 5 | Commutative Property of Addition |

---

📌 Note on #9: If this is from a printed worksheet and you’re submitting answers, you may want to note that the equation as written is false, but the *intended property* is likely Commutative Property of Addition.

---

Let me know if you’d like this formatted for printing or turned into a fill-in-the-blank answer key! 😊