https://file.aiquickdraw.com/mathbot/file/1725734578840ws2t4urx.jpg

It seems that there is an issue with processing the Arabic text in the image. However, I can analyze the mathematical expressions directly from the image visually.

From what I see, this image contains a set of ratios and proportion problems in Arabic. Let's solve them step by step.

### First problem set (on the left side):

1. **First ratio problem:**
   \[
   \frac{4}{x} = \frac{7}{20}
   \]

   Cross-multiply to solve for \( x \):
   \[
   4 \times 20 = 7 \times x
   \]
   \[
   80 = 7x \quad \Rightarrow \quad x = \frac{80}{7} \approx 11.43
   \]

2. **Second ratio problem:**
   \[
   \frac{35}{x} = \frac{7}{12}
   \]

   Cross-multiply:
   \[
   35 \times 12 = 7 \times x
   \]
   \[
   420 = 7x \quad \Rightarrow \quad x = \frac{420}{7} = 60
   \]

3. **Third ratio problem:**
   \[
   \frac{x}{21} = \frac{8}{12}
   \]

   Cross-multiply:
   \[
   x \times 12 = 8 \times 21
   \]
   \[
   12x = 168 \quad \Rightarrow \quad x = \frac{168}{12} = 14
   \]

### Second problem set (on the right side):

1. **First ratio problem:**
   \[
   \frac{15}{x} = \frac{3}{4}
   \]

   Cross-multiply:
   \[
   15 \times 4 = 3 \times x
   \]
   \[
   60 = 3x \quad \Rightarrow \quad x = \frac{60}{3} = 20
   \]

2. **Second ratio problem:**
   \[
   \frac{x}{14} = \frac{6}{9}
   \]

   Cross-multiply:
   \[
   x \times 9 = 6 \times 14
   \]
   \[
   9x = 84 \quad \Rightarrow \quad x = \frac{84}{9} = 9.33
   \]

3. **Third ratio problem:**
   \[
   \frac{a}{16} = \frac{5}{4}
   \]

   Cross-multiply:
   \[
   a \times 4 = 5 \times 16
   \]
   \[
   4a = 80 \quad \Rightarrow \quad a = \frac{80}{4} = 20
   \]

Would you like more details on any of the steps? Here are a few questions to expand your understanding:

1. How does cross-multiplication work in ratio problems?
2. How do we simplify ratios after solving them?
3. What are common mistakes to avoid in ratio and proportion problems?
4. How are ratios used in real-life applications?
5. How do you handle cases when one side of the ratio involves decimals or fractions?

**Tip:** Always reduce ratios to their simplest form for better understanding and application.

Solve the given ratio and proportion problems.

Learn how to solve ratio and proportion problems using cross-multiplication. This lesson covers ratios, proportions, and key algebraic concepts. Suitable for students in Grades 6-8.

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