Multiplication of Positive and Negative Integers Worksheet for 7th ... - Free Printable

Problem Description:

The image shows a worksheet titled "Multiplication Positive/Negative," which involves solving multiplication problems involving positive and negative integers. The task is to compute the results of these multiplications and understand the rules governing the signs of the products.

Solution and Explanation:

#### Key Rules for Multiplying Positive and Negative Numbers:
1. Positive × Positive = Positive: The product of two positive numbers is always positive.
2. Negative × Negative = Positive: The product of two negative numbers is always positive.
3. Positive × Negative = Negative: The product of a positive number and a negative number is always negative.
4. Negative × Positive = Negative: The product of a negative number and a positive number is always negative.

Now, let's solve each problem step by step:

---

#### 1. $-8 \times 4$
- Rule: Negative × Positive = Negative
- Calculation: $8 \times 4 = 32$
- Result: $-32$

#### 2. $-3 \times 1$
- Rule: Negative × Positive = Negative
- Calculation: $3 \times 1 = 3$
- Result: $-3$

#### 3. $-8 \times 7$
- Rule: Negative × Positive = Negative
- Calculation: $8 \times 7 = 56$
- Result: $-56$

#### 4. $-1 \times -1$
- Rule: Negative × Negative = Positive
- Calculation: $1 \times 1 = 1$
- Result: $1$

---

#### 5. $7 \times -9$
- Rule: Positive × Negative = Negative
- Calculation: $7 \times 9 = 63$
- Result: $-63$

#### 6. $-3 \times -9$
- Rule: Negative × Negative = Positive
- Calculation: $3 \times 9 = 27$
- Result: $27$

#### 7. $9 \times 0$
- Rule: Any number multiplied by 0 is 0
- Calculation: $9 \times 0 = 0$
- Result: $0$

#### 8. $2 \times 9$
- Rule: Positive × Positive = Positive
- Calculation: $2 \times 9 = 18$
- Result: $18$

---

#### 9. $-8 \times -8$
- Rule: Negative × Negative = Positive
- Calculation: $8 \times 8 = 64$
- Result: $64$

#### 10. $-4 \times 3$
- Rule: Negative × Positive = Negative
- Calculation: $4 \times 3 = 12$
- Result: $-12$

#### 11. $2 \times 7$
- Rule: Positive × Positive = Positive
- Calculation: $2 \times 7 = 14$
- Result: $14$

#### 12. $-2 \times -9$
- Rule: Negative × Negative = Positive
- Calculation: $2 \times 9 = 18$
- Result: $18$

---

#### 13. $3 \times 9$
- Rule: Positive × Positive = Positive
- Calculation: $3 \times 9 = 27$
- Result: $27$

#### 14. $7 \times 7$
- Rule: Positive × Positive = Positive
- Calculation: $7 \times 7 = 49$
- Result: $49$

#### 15. $7 \times -2$
- Rule: Positive × Negative = Negative
- Calculation: $7 \times 2 = 14$
- Result: $-14$

#### 16. $-1 \times -1$
- Rule: Negative × Negative = Positive
- Calculation: $1 \times 1 = 1$
- Result: $1$

---

#### 17. $8 \times -3$
- Rule: Positive × Negative = Negative
- Calculation: $8 \times 3 = 24$
- Result: $-24$

#### 18. $-1 \times 7$
- Rule: Negative × Positive = Negative
- Calculation: $1 \times 7 = 7$
- Result: $-7$

#### 19. $0 \times 7$
- Rule: Any number multiplied by 0 is 0
- Calculation: $0 \times 7 = 0$
- Result: $0$

#### 20. $-6 \times 6$
- Rule: Negative × Positive = Negative
- Calculation: $6 \times 6 = 36$
- Result: $-36$

---

#### 21. $0 \times 6$
- Rule: Any number multiplied by 0 is 0
- Calculation: $0 \times 6 = 0$
- Result: $0$

#### 22. $3 \times 7$
- Rule: Positive × Positive = Positive
- Calculation: $3 \times 7 = 21$
- Result: $21$

#### 23. $-1 \times -6$
- Rule: Negative × Negative = Positive
- Calculation: $1 \times 6 = 6$
- Result: $6$

#### 24. $0 \times 0$
- Rule: Any number multiplied by 0 is 0
- Calculation: $0 \times 0 = 0$
- Result: $0$

---

#### 25. $5 \times -8$
- Rule: Positive × Negative = Negative
- Calculation: $5 \times 8 = 40$
- Result: $-40$

#### 26. $-4 \times -2$
- Rule: Negative × Negative = Positive
- Calculation: $4 \times 2 = 8$
- Result: $8$

#### 27. $3 \times -2$
- Rule: Positive × Negative = Negative
- Calculation: $3 \times 2 = 6$
- Result: $-6$

#### 28. $-1 \times -9$
- Rule: Negative × Negative = Positive
- Calculation: $1 \times 9 = 9$
- Result: $9$

---

#### 29. $7 \times -7$
- Rule: Positive × Negative = Negative
- Calculation: $7 \times 7 = 49$
- Result: $-49$

#### 30. $-5 \times 1$
- Rule: Negative × Positive = Negative
- Calculation: $5 \times 1 = 5$
- Result: $-5$

#### 31. $8 \times 1$
- Rule: Positive × Positive = Positive
- Calculation: $8 \times 1 = 8$
- Result: $8$

#### 32. $7 \times 1$
- Rule: Positive × Positive = Positive
- Calculation: $7 \times 1 = 7$
- Result: $7$

---

Final Answer:

The completed worksheet with all solutions is as follows:

| Expression | Result |
|------------------|--------|
| $-8 \times 4$ | $-32$ |
| $-3 \times 1$ | $-3$ |
| $-8 \times 7$ | $-56$ |
| $-1 \times -1$ | $1$ |
| $7 \times -9$ | $-63$ |
| $-3 \times -9$ | $27$ |
| $9 \times 0$ | $0$ |
| $2 \times 9$ | $18$ |
| $-8 \times -8$ | $64$ |
| $-4 \times 3$ | $-12$ |
| $2 \times 7$ | $14$ |
| $-2 \times -9$ | $18$ |
| $3 \times 9$ | $27$ |
| $7 \times 7$ | $49$ |
| $7 \times -2$ | $-14$ |
| $-1 \times -1$ | $1$ |
| $8 \times -3$ | $-24$ |
| $-1 \times 7$ | $-7$ |
| $0 \times 7$ | $0$ |
| $-6 \times 6$ | $-36$ |
| $0 \times 6$ | $0$ |
| $3 \times 7$ | $21$ |
| $-1 \times -6$ | $6$ |
| $0 \times 0$ | $0$ |
| $5 \times -8$ | $-40$ |
| $-4 \times -2$ | $8$ |
| $3 \times -2$ | $-6$ |
| $-1 \times -9$ | $9$ |
| $7 \times -7$ | $-49$ |
| $-5 \times 1$ | $-5$ |
| $8 \times 1$ | $8$ |
| $7 \times 1$ | $7$ |

$$
\boxed{-32, -3, -56, 1, -63, 27, 0, 18, 64, -12, 14, 18, 27, 49, -14, 1, -24, -7, 0, -36, 0, 21, 6, 0, -40, 8, -6, 9, -49, -5, 8, 7}
$$