Practice: Multiplying Integers worksheet - Free Printable

Problem: Multiplying Integers

The task involves solving a series of integer multiplication problems. Here are the steps to solve each problem, along with explanations.

---

#### Rules for Multiplying Integers:
1. Positive × Positive = Positive: The product of two positive integers is always positive.
2. Negative × Negative = Positive: The product of two negative integers is always positive.
3. Positive × Negative = Negative: The product of a positive integer and a negative integer is always negative.
4. Any number × 0 = 0: Multiplying any integer by zero results in zero.

---

Solutions:

#### 1. (+5) × (+6)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 5 \times 6 = 30 \)
- Answer: \( +30 \)

#### 2. (+8) × (+8)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 8 \times 8 = 64 \)
- Answer: \( +64 \)

#### 3. (+9) × (0)
- Any number multiplied by zero is zero.
- Answer: \( 0 \)

#### 4. (−3) × (+1)
- One number is negative, and the other is positive.
- Negative × Positive = Negative
- \( 3 \times 1 = 3 \), but the result is negative.
- Answer: \( -3 \)

#### 5. (+3) × (+8)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 3 \times 8 = 24 \)
- Answer: \( +24 \)

#### 6. (−3) × (−6)
- Both numbers are negative.
- Negative × Negative = Positive
- \( 3 \times 6 = 18 \)
- Answer: \( +18 \)

#### 7. (−6) × (+8)
- One number is negative, and the other is positive.
- Negative × Positive = Negative
- \( 6 \times 8 = 48 \), but the result is negative.
- Answer: \( -48 \)

#### 8. (−8) × (+8)
- One number is negative, and the other is positive.
- Negative × Positive = Negative
- \( 8 \times 8 = 64 \), but the result is negative.
- Answer: \( -64 \)

#### 9. (+3) × (+7)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 3 \times 7 = 21 \)
- Answer: \( +21 \)

#### 10. (+6) × (−5)
- One number is positive, and the other is negative.
- Positive × Negative = Negative
- \( 6 \times 5 = 30 \), but the result is negative.
- Answer: \( -30 \)

#### 11. (−4) × (−3)
- Both numbers are negative.
- Negative × Negative = Positive
- \( 4 \times 3 = 12 \)
- Answer: \( +12 \)

#### 12. (−8) × (0)
- Any number multiplied by zero is zero.
- Answer: \( 0 \)

#### 13. (−4) × (+1)
- One number is negative, and the other is positive.
- Negative × Positive = Negative
- \( 4 \times 1 = 4 \), but the result is negative.
- Answer: \( -4 \)

#### 14. (+8) × (+7)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 8 \times 7 = 56 \)
- Answer: \( +56 \)

#### 15. (+1) × (+2)
- Both numbers are positive.
- Positive × Positive = Positive
- \( 1 \times 2 = 2 \)
- Answer: \( +2 \)

---

Final Answers:

1. \( +30 \)
2. \( +64 \)
3. \( 0 \)
4. \( -3 \)
5. \( +24 \)
6. \( +18 \)
7. \( -48 \)
8. \( -64 \)
9. \( +21 \)
10. \( -30 \)
11. \( +12 \)
12. \( 0 \)
13. \( -4 \)
14. \( +56 \)
15. \( +2 \)

---

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \, +30 \\
2. & \, +64 \\
3. & \, 0 \\
4. & \, -3 \\
5. & \, +24 \\
6. & \, +18 \\
7. & \, -48 \\
8. & \, -64 \\
9. & \, +21 \\
10. & \, -30 \\
11. & \, +12 \\
12. & \, 0 \\
13. & \, -4 \\
14. & \, +56 \\
15. & \, +2 \\
\end{aligned}
}
\]