Multiplying Integers worksheet with math problems and playful illustrations.

Problem: Multiplying Integers

The task involves solving a series of integer multiplication problems. Let's go through each problem step by step and explain the rules for multiplying integers.

#### 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.

Now, let's solve each problem:

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Problem 1: (+5) × (+6)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 5 \times 6 = 30 \).

Answer: \( +30 \)

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Problem 2: (+8) × (+8)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 8 \times 8 = 64 \).

Answer: \( +64 \)

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Problem 3: (+9) × (0)

- Any number multiplied by zero is zero.
- Calculation: \( 9 \times 0 = 0 \).

Answer: \( 0 \)

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Problem 4: (−3) × (+1)

- One number is negative, and the other is positive.
- According to the rule: Positive × Negative = Negative.
- Calculation: \( -3 \times 1 = -3 \).

Answer: \( -3 \)

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Problem 5: (+3) × (+8)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 3 \times 8 = 24 \).

Answer: \( +24 \)

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Problem 6: (−3) × (−6)

- Both numbers are negative.
- According to the rule: Negative × Negative = Positive.
- Calculation: \( -3 \times -6 = 18 \).

Answer: \( +18 \)

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Problem 7: (−6) × (+8)

- One number is negative, and the other is positive.
- According to the rule: Positive × Negative = Negative.
- Calculation: \( -6 \times 8 = -48 \).

Answer: \( -48 \)

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Problem 8: (−8) × (+8)

- One number is negative, and the other is positive.
- According to the rule: Positive × Negative = Negative.
- Calculation: \( -8 \times 8 = -64 \).

Answer: \( -64 \)

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Problem 9: (+3) × (+7)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 3 \times 7 = 21 \).

Answer: \( +21 \)

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Problem 10: (+6) × (−5)

- One number is positive, and the other is negative.
- According to the rule: Positive × Negative = Negative.
- Calculation: \( 6 \times -5 = -30 \).

Answer: \( -30 \)

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Problem 11: (−4) × (−3)

- Both numbers are negative.
- According to the rule: Negative × Negative = Positive.
- Calculation: \( -4 \times -3 = 12 \).

Answer: \( +12 \)

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Problem 12: (−8) × (0)

- Any number multiplied by zero is zero.
- Calculation: \( -8 \times 0 = 0 \).

Answer: \( 0 \)

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Problem 13: (−4) × (+1)

- One number is negative, and the other is positive.
- According to the rule: Positive × Negative = Negative.
- Calculation: \( -4 \times 1 = -4 \).

Answer: \( -4 \)

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Problem 14: (+8) × (+7)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 8 \times 7 = 56 \).

Answer: \( +56 \)

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Problem 15: (+1) × (+2)

- Both numbers are positive.
- According to the rule: Positive × Positive = Positive.
- Calculation: \( 1 \times 2 = 2 \).

Answer: \( +2 \)

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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{
\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}
}