Solving Proportions Worksheet for 9th Grade | Lesson Planet - Free Printable

You’ve uploaded a worksheet titled “SOLVING PROPORTIONS” that teaches how to solve proportions using cross-multiplication. Let’s walk through the concept, solve the example problems, and then provide answers to all the exercises with explanations.

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## ✔ What is a Proportion?

A proportion is an equation stating that two ratios (fractions) are equal:

> a/b = c/d

To solve for a missing value (usually denoted by x), we use cross-multiplication:

> a × d = b × c

This works because if two fractions are equal, their cross-products are equal.

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## 📘 Example 1: Solve for x

> 7 / 8 = x / 4

Step-by-step:

1. Cross-multiply:
→ 7 × 4 = 8 × x
→ 28 = 8x

2. Solve for x:
→ x = 28 ÷ 8
→ x = 3.5 or 7/2

✔ Answer: x = 7/2 or 3.5

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## 📘 Example 2: Solve for x

> 3 / 4 = 5 / (2x + 1)

Step-by-step:

1. Cross-multiply:
→ 3 × (2x + 1) = 4 × 5
→ 6x + 3 = 20

2. Subtract 3 from both sides:
→ 6x = 17

3. Divide by 6:
→ x = 17/6

✔ Answer: x = 17/6

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## 📝 Now let’s solve all the problems from the worksheet:

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Problems 1–15:

We’ll solve each one using cross-multiplication.

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#### 1. x/5 = 3/15

Cross-multiply:
→ 15x = 5 × 3 = 15
→ x = 15 ÷ 15 = 1

✔ Answer: 1

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#### 2. x/9 = 4/12

Cross-multiply:
→ 12x = 9 × 4 = 36
→ x = 36 ÷ 12 = 3

✔ Answer: 3

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#### 3. x/8 = 3/12

Cross-multiply:
→ 12x = 8 × 3 = 24
→ x = 24 ÷ 12 = 2

✔ Answer: 2

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#### 4. x/6 = 5/10

Cross-multiply:
→ 10x = 6 × 5 = 30
→ x = 30 ÷ 10 = 3

✔ Answer: 3

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#### 5. x/7 = 2/14

Cross-multiply:
→ 14x = 7 × 2 = 14
→ x = 14 ÷ 14 = 1

✔ Answer: 1

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#### 6. x/10 = 3/15

Cross-multiply:
→ 15x = 10 × 3 = 30
→ x = 30 ÷ 15 = 2

✔ Answer: 2

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#### 7. x/12 = 4/16

Cross-multiply:
→ 16x = 12 × 4 = 48
→ x = 48 ÷ 16 = 3

✔ Answer: 3

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#### 8. x/15 = 5/25

Cross-multiply:
→ 25x = 15 × 5 = 75
→ x = 75 ÷ 25 = 3

✔ Answer: 3

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#### 9. x/18 = 6/24

Cross-multiply:
→ 24x = 18 × 6 = 108
→ x = 108 ÷ 24 = 4.5 or 9/2

✔ Answer: 9/2

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#### 10. x/20 = 4/10

Cross-multiply:
→ 10x = 20 × 4 = 80
→ x = 80 ÷ 10 = 8

✔ Answer: 8

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#### 11. x/24 = 8/32

Cross-multiply:
→ 32x = 24 × 8 = 192
→ x = 192 ÷ 32 = 6

✔ Answer: 6

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#### 12. x/30 = 6/15

Cross-multiply:
→ 15x = 30 × 6 = 180
→ x = 180 ÷ 15 = 12

✔ Answer: 12

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#### 13. x/36 = 9/45

Cross-multiply:
→ 45x = 36 × 9 = 324
→ x = 324 ÷ 45 = 7.2 or 36/5

✔ Answer: 36/5

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#### 14. x/40 = 8/20

Cross-multiply:
→ 20x = 40 × 8 = 320
→ x = 320 ÷ 20 = 16

✔ Answer: 16

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#### 15. x/45 = 9/15

Cross-multiply:
→ 15x = 45 × 9 = 405
→ x = 405 ÷ 15 = 27

✔ Answer: 27

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## ✔ Final Answers (as listed in the worksheet):

The worksheet already provides the answers at the bottom — here they are again for clarity:

> Answers:
> 1. 1
> 2. 3
> 3. 2
> 4. 3
> 5. 1
> 6. 2
> 7. 3
> 8. 3
> 9. 9/2
> 10. 8
> 11. 6
> 12. 12
> 13. 36/5
> 14. 16
> 15. 27

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## 🧠 Key Takeaway:

- Always set up the proportion correctly.
- Use cross-multiplication: multiply numerator of first fraction by denominator of second, and vice versa.
- Solve the resulting equation for the variable.
- Simplify your answer if needed (as a fraction or decimal).

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Let me know if you’d like to see these solved visually or want to practice more! 😊