Multiply and Divide Integers | Interactive Worksheet - Free Printable

The task involves solving a series of multiplication and division problems with integers. Below, I will solve each problem step by step and explain the rules for multiplying and dividing integers.

Rules for Multiplying and Dividing Integers:

1. Same Signs: The result is positive.
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive

2. Different Signs: The result is negative.
- Positive × Negative = Negative
- Negative × Positive = Negative
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative

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Solutions:

#### 1. $-5 \times 9$
- Multiply $-5$ and $9$.
- Different signs: Result is negative.
- $-5 \times 9 = -45$

#### 2. $-50 \div (-5)$
- Divide $-50$ by $-5$.
- Same signs: Result is positive.
- $-50 \div (-5) = 10$

#### 3. $6 \times (-8)$
- Multiply $6$ and $-8$.
- Different signs: Result is negative.
- $6 \times (-8) = -48$

#### 4. $32 \div (-4)$
- Divide $32$ by $-4$.
- Different signs: Result is negative.
- $32 \div (-4) = -8$

#### 5. $-7 \times (-3)$
- Multiply $-7$ and $-3$.
- Same signs: Result is positive.
- $-7 \times (-3) = 21$

#### 6. $-63 \div 7$
- Divide $-63$ by $7$.
- Different signs: Result is negative.
- $-63 \div 7 = -9$

#### 7. $8 \times (-5)$
- Multiply $8$ and $-5$.
- Different signs: Result is negative.
- $8 \times (-5) = -40$

#### 8. $81 \div (-9)$
- Divide $81$ by $-9$.
- Different signs: Result is negative.
- $81 \div (-9) = -9$

#### 9. $-6 \times 10$
- Multiply $-6$ and $10$.
- Different signs: Result is negative.
- $-6 \times 10 = -60$

#### 10. $-17 \times 6$
- Multiply $-17$ and $6$.
- Different signs: Result is negative.
- $-17 \times 6 = -102$

#### 11. $7 \times (-4)$
- Multiply $7$ and $-4$.
- Different signs: Result is negative.
- $7 \times (-4) = -28$

#### 12. $-33 \div (-3)$
- Divide $-33$ by $-3$.
- Same signs: Result is positive.
- $-33 \div (-3) = 11$

#### 13. $-24 \div (-2)$
- Divide $-24$ by $-2$.
- Same signs: Result is positive.
- $-24 \div (-2) = 12$

#### 14. $-9 \div (-3)$
- Divide $-9$ by $-3$.
- Same signs: Result is positive.
- $-9 \div (-3) = 3$

#### 15. $-56 \div 7$
- Divide $-56$ by $7$.
- Different signs: Result is negative.
- $-56 \div 7 = -8$

#### 16. $-10 \div 10$
- Divide $-10$ by $10$.
- Different signs: Result is negative.
- $-10 \div 10 = -1$

#### 17. $-20 \div (-2)$
- Divide $-20$ by $-2$.
- Same signs: Result is positive.
- $-20 \div (-2) = 10$

#### 18. $560 \div (-7)$
- Divide $560$ by $-7$.
- Different signs: Result is negative.
- $560 \div (-7) = -80$

#### 19. $30 \div (-6)$
- Divide $30$ by $-6$.
- Different signs: Result is negative.
- $30 \div (-6) = -5$

#### 20. $-240 \div 12$
- Divide $-240$ by $12$.
- Different signs: Result is negative.
- $-240 \div 12 = -20$

#### 21. $150 \div (-30)$
- Divide $150$ by $-30$.
- Different signs: Result is negative.
- $150 \div (-30) = -5$

#### 22. $-40 \times (-60)$
- Multiply $-40$ and $-60$.
- Same signs: Result is positive.
- $-40 \times (-60) = 2400$

#### 23. $-250 \div 5$
- Divide $-250$ by $5$.
- Different signs: Result is negative.
- $-250 \div 5 = -50$

#### 24. $-30 \div (-40)$
- Divide $-30$ by $-40$.
- Same signs: Result is positive.
- $-30 \div (-40) = \frac{3}{4}$ or $0.75$

#### 25. $-500 \times 7$
- Multiply $-500$ and $7$.
- Different signs: Result is negative.
- $-500 \times 7 = -3500$

#### 26. $600 \div (-5)$
- Divide $600$ by $-5$.
- Different signs: Result is negative.
- $600 \div (-5) = -120$

#### 27. $-640 \div (-80)$
- Divide $-640$ by $-80$.
- Same signs: Result is positive.
- $-640 \div (-80) = 8$

#### 28. $-210 \div (-3)$
- Divide $-210$ by $-3$.
- Same signs: Result is positive.
- $-210 \div (-3) = 70$

#### 29. $900 \div (-7)$
- Divide $900$ by $-7$.
- Different signs: Result is negative.
- $900 \div (-7) = -\frac{900}{7} \approx -128.57$

#### 30. $-200 \div 4$
- Divide $-200$ by $4$.
- Different signs: Result is negative.
- $-200 \div 4 = -50$

#### 31. $-4 \times (-64)$
- Multiply $-4$ and $-64$.
- Same signs: Result is positive.
- $-4 \times (-64) = 256$

#### 32. $-574 \div 7$
- Divide $-574$ by $7$.
- Different signs: Result is negative.
- $-574 \div 7 = -82$

#### 33. $276 \div (-6)$
- Divide $276$ by $-6$.
- Different signs: Result is negative.
- $276 \div (-6) = -46$

#### 34. $7 \div (-5)$
- Divide $7$ by $-5$.
- Different signs: Result is negative.
- $7 \div (-5) = -\frac{7}{5} = -1.4$

#### 35. $-152 \div (-8)$
- Divide $-152$ by $-8$.
- Same signs: Result is positive.
- $-152 \div (-8) = 19$

#### 36. $0 \times 81$
- Multiply $0$ and $81$.
- Any number multiplied by $0$ is $0$.
- $0 \times 81 = 0$

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Final Answers:

$$
\boxed{
\begin{array}{ll}
1. & -45 \\
2. & 10 \\
3. & -48 \\
4. & -8 \\
5. & 21 \\
6. & -9 \\
7. & -40 \\
8. & -9 \\
9. & -60 \\
10. & -102 \\
11. & -28 \\
12. & 11 \\
13. & 12 \\
14. & 3 \\
15. & -8 \\
16. & -1 \\
17. & 10 \\
18. & -80 \\
19. & -5 \\
20. & -20 \\
21. & -5 \\
22. & 2400 \\
23. & -50 \\
24. & 0.75 \\
25. & -3500 \\
26. & -120 \\
27. & 8 \\
28. & 70 \\
29. & -128.57 \\
30. & -50 \\
31. & 256 \\
32. & -82 \\
33. & -46 \\
34. & -1.4 \\
35. & 19 \\
36. & 0 \\
\end{array}
}
$$