https://file.aiquickdraw.com/mathbot/file/1728827814366jv89xn9m.jpg

The image shows a series of fractions with missing values, likely requiring the completion of proportions. Let's solve each one.

### 1. \( \frac{6}{4} = \frac{2}{3} \)
We can solve for the missing part by cross-multiplying:
\[
6 \times 3 = 4 \times 2
\]
This gives \( 18 = 8 \), which is not possible. So, the first one may be incorrect or unsolvable with the given numbers.

### 2. \( \frac{5}{3} = \frac{4}{4} \)
In this case:
\[
5 \times 4 = 3 \times 4
\]
This simplifies to \( 20 = 12 \), which is also not possible.

### 3. \( \frac{8}{5} = \frac{9}{2} \)
Cross-multiplying:
\[
8 \times 2 = 5 \times 9
\]
This gives:
\[
16 = 45
\]
This also leads to an impossible equality, suggesting that this proportion isn't correct either.

### 4. \( \frac{10}{2} = \frac{C}{3} \)
Cross-multiplying:
\[
10 \times 3 = 2 \times C
\]
This gives \( 30 = 2C \), so \( C = 15 \).

### 5. \( \frac{4}{2} = \frac{8}{4} \)
Cross-multiplying:
\[
4 \times 4 = 2 \times 8
\]
This simplifies to:
\[
16 = 16
\]
This equation is correct.

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Let me know if you need further details on any of these calculations, or if you'd like clarification on the problematic ones.

Here are 5 related questions to expand your understanding:
1. How can we verify if a proportion is valid?
2. What are the steps for solving missing values in proportions?
3. How does cross-multiplication work in solving ratios?
4. What are some common mistakes when setting up proportion problems?
5. How are proportions applied in real-life situations like scaling recipes?

**Tip:** Always double-check the given values in proportions before solving, especially when they lead to seemingly impossible results.

The image shows a series of proportion problems with missing values. The task is to complete the proportions and find missing variables where required.

Learn how to solve a series of proportions involving missing values using cross-multiplication. This problem covers concepts like fractions, ratios, and the proportion theorem, suitable for students in Grades 6-8.

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