Rational Numbers Worksheet for 8th - 9th Grade | Lesson Planet - Free Printable

It looks like you've uploaded a worksheet titled "Multiplying Rational Numbers" with several problems involving multiplication of fractions, decimals, and integers. Since I can't view images directly, I’ll guide you through solving the problems step by step based on the text you provided.

Let me go through each problem and solve it with explanations.

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Part A: Multiply

1. $-4 \cdot (-7)$

- Multiplying two negative numbers gives a positive result.
- $-4 \cdot (-7) = 28$

✔ Answer: 28

2. $8 \cdot (-0.7)$

- Multiply 8 and 0.7: $8 \cdot 0.7 = 5.6$
- Since one number is negative, the result is negative.
- $8 \cdot (-0.7) = -5.6$

✔ Answer: -5.6

3. $26 \cdot (-7)$

- $26 \cdot 7 = 182$, and since one number is negative:
- $26 \cdot (-7) = -182$

✔ Answer: -182

4. $-6 \cdot \left(-\frac{1}{3}\right)$

- Negative × negative = positive
- $6 \cdot \frac{1}{3} = 2$
- So, $-6 \cdot \left(-\frac{1}{3}\right) = 2$

✔ Answer: 2

5. $-4.4 \cdot (-2.3)$

- Both negative → positive result
- $4.4 \cdot 2.3 = ?$
- $4.4 \cdot 2 = 8.8$
- $4.4 \cdot 0.3 = 1.32$
- Total: $8.8 + 1.32 = 10.12$
- So, $-4.4 \cdot (-2.3) = 10.12$

✔ Answer: 10.12

6. $-1.1 \cdot (-2.5) \cdot (-1)$

- First, multiply $-1.1 \cdot (-2.5) = 2.75$ (negative × negative = positive)
- Then $2.75 \cdot (-1) = -2.75$

✔ Answer: -2.75

7. $\frac{1}{2} \cdot \left(-\frac{2}{3}\right)$

- Multiply numerators: $1 \cdot (-2) = -2$
- Multiply denominators: $2 \cdot 3 = 6$
- $\frac{-2}{6} = -\frac{1}{3}$

✔ Answer: $-\frac{1}{3}$

8. $\frac{2}{3} \cdot (-0.9)$

- Convert $-0.9$ to fraction: $-\frac{9}{10}$
- $\frac{2}{3} \cdot \left(-\frac{9}{10}\right) = \frac{-18}{30} = -\frac{3}{5}$

✔ Answer: $-\frac{3}{5}$

9. $-1 \cdot \left(-\frac{1}{2}\right) \cdot (-1.5)$

- Step-by-step:
- $-1 \cdot \left(-\frac{1}{2}\right) = \frac{1}{2}$
- $\frac{1}{2} \cdot (-1.5) = \frac{1}{2} \cdot \left(-\frac{3}{2}\right) = -\frac{3}{4}$

✔ Answer: $-\frac{3}{4}$

10. $(-0.5) \cdot (-0.1)$

- Negative × negative = positive
- $0.5 \cdot 0.1 = 0.05$

✔ Answer: 0.05

11. $-2 \cdot \left(-\frac{1}{4}\right) \cdot (-1.5)$

- Step-by-step:
- $-2 \cdot \left(-\frac{1}{4}\right) = \frac{2}{4} = \frac{1}{2}$
- $\frac{1}{2} \cdot (-1.5) = \frac{1}{2} \cdot \left(-\frac{3}{2}\right) = -\frac{3}{4}$

✔ Answer: $-\frac{3}{4}$

12. $\frac{3}{4} \cdot \left(-\frac{1}{2}\right) \cdot (-1)$

- $\frac{3}{4} \cdot \left(-\frac{1}{2}\right) = -\frac{3}{8}$
- $-\frac{3}{8} \cdot (-1) = \frac{3}{8}$

✔ Answer: $\frac{3}{8}$

13. $\frac{1}{2} \cdot (-0.8) \cdot (-2)$

- First: $\frac{1}{2} \cdot (-0.8) = -0.4$
- Then: $-0.4 \cdot (-2) = 0.8$

✔ Answer: 0.8

14. $\frac{1}{4} \cdot (-1.2) \cdot (-1.2)$

- First: $\frac{1}{4} \cdot (-1.2) = -0.3$
- Then: $-0.3 \cdot (-1.2) = 0.36$

✔ Answer: 0.36

15. $\frac{1}{2} \cdot \left(-\frac{2}{3}\right) \cdot (-1)$

- $\frac{1}{2} \cdot \left(-\frac{2}{3}\right) = -\frac{2}{6} = -\frac{1}{3}$
- $-\frac{1}{3} \cdot (-1) = \frac{1}{3}$

✔ Answer: $\frac{1}{3}$

16. $\frac{1}{2} \cdot (-0.8) \cdot (-2)$

- Same as #13 → $0.8$

✔ Answer: 0.8

17. $-3 \cdot \left(\frac{1}{3}\right) \cdot (-2)$

- $-3 \cdot \frac{1}{3} = -1$
- $-1 \cdot (-2) = 2$

✔ Answer: 2

18. $\frac{1}{2} \cdot (-0.8) \cdot (-2)$

- Again same as #13 → $0.8$

✔ Answer: 0.8

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Simplify:

19. $-3 \cdot (-5) \cdot (-2)(4)$

- Group: $(-3) \cdot (-5) = 15$
- $15 \cdot (-2) = -30$
- $-30 \cdot 4 = -120$

✔ Answer: -120

20. $(-1.2)(-0.5) \cdot (-4) \cdot (-4.5)(-2)$

- Step-by-step:
- $(-1.2)(-0.5) = 0.6$
- $0.6 \cdot (-4) = -2.4$
- $-2.4 \cdot (-4.5) = 10.8$
- $10.8 \cdot (-2) = -21.6$

✔ Answer: -21.6

21. $(-2.5)(-3) \cdot (-4) \cdot (-4.5)(-2)$

- $(-2.5)(-3) = 7.5$
- $7.5 \cdot (-4) = -30$
- $-30 \cdot (-4.5) = 135$
- $135 \cdot (-2) = -270$

✔ Answer: -270

22. $-10 \cdot (-3)$

- Negative × negative = positive
- $10 \cdot 3 = 30$

✔ Answer: 30

23. $-5(10) \cdot (-10) \cdot 2(10)$

- First: $-5 \cdot 10 = -50$
- $-50 \cdot (-10) = 500$
- $500 \cdot 2 = 1000$
- $1000 \cdot 10 = 10,000$

✔ Answer: 10,000

24. $-2(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- $-2 \cdot 1.5 = -3$
- $-3 \cdot (-1) = 3$
- $3 \cdot (-2.5) = -7.5$
- $-7.5 \cdot 2.5 = -18.75$

✔ Answer: -18.75

25. $-2(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- Same as above → $-18.75$

✔ Answer: -18.75

26. $-10(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- $-10 \cdot 1.5 = -15$
- $-15 \cdot (-1) = 15$
- $15 \cdot (-2.5) = -37.5$
- $-37.5 \cdot 2.5 = -93.75$

✔ Answer: -93.75

27. $-2(10) \cdot (-10) \cdot 2(10)$

- $-2 \cdot 10 = -20$
- $-20 \cdot (-10) = 200$
- $200 \cdot 2 = 400$
- $400 \cdot 10 = 4,000$

✔ Answer: 4,000

28. $-3(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- $-3 \cdot 1.5 = -4.5$
- $-4.5 \cdot (-1) = 4.5$
- $4.5 \cdot (-2.5) = -11.25$
- $-11.25 \cdot 2.5 = -28.125$

✔ Answer: -28.125

29. $-2(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- Already solved → $-18.75$

✔ Answer: -18.75

30. $-2(1.5) \cdot (-1) \cdot (-2.5)(2.5)$

- Same as above → $-18.75$

✔ Answer: -18.75

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 28 |
| 2 | -5.6 |
| 3 | -182 |
| 4 | 2 |
| 5 | 10.12 |
| 6 | -2.75 |
| 7 | $-\frac{1}{3}$ |
| 8 | $-\frac{3}{5}$ |
| 9 | $-\frac{3}{4}$ |
| 10 | 0.05 |
| 11 | $-\frac{3}{4}$ |
| 12 | $\frac{3}{8}$ |
| 13 | 0.8 |
| 14 | 0.36 |
| 15 | $\frac{1}{3}$ |
| 16 | 0.8 |
| 17 | 2 |
| 18 | 0.8 |
| 19 | -120 |
| 20 | -21.6 |
| 21 | -270 |
| 22 | 30 |
| 23 | 10,000 |
| 24 | -18.75 |
| 25 | -18.75 |
| 26 | -93.75 |
| 27 | 4,000 |
| 28 | -28.125 |
| 29 | -18.75 |
| 30 | -18.75 |

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