https://r2.erweima.ai/mathbot/image/17179515246303v10rw5o.png

The OCR results were not very accurate. I will manually extract and analyze the fractions from the image.

Here is the extracted table with identified fractions and spaces for missing values:

\[
\begin{array}{|c|c|c|c|}
\hline
\frac{1}{2} & \frac{1}{4} & \frac{1}{5} & \frac{19}{20} \\
\hline
\text{?} & \frac{2}{7} & \frac{2}{7} & \frac{19}{21} \\
\hline
\frac{2}{4} & \text{?} & \frac{3}{5} & \text{?} \\
\hline
\frac{4}{3} & \frac{101}{84} & \text{?} & \frac{507}{140} \\
\hline
\end{array}
\]

Let's analyze the patterns for each column:

### First Column
\[
\frac{1}{2}, \text{?}, \frac{2}{4}, \frac{4}{3}
\]
The pattern here appears to be an arithmetic or geometric progression. Simplifying, \(\frac{2}{4} = \frac{1}{2}\) and then:
\[
\frac{4}{3} \rightarrow \frac{4}{2} = 2
\]

### Second Column
\[
\frac{1}{4}, \frac{2}{7}, \text{?}, \frac{101}{84}
\]
This column is less obvious but we notice that:
\[
\frac{1}{4} = 0.25, \frac{2}{7} \approx 0.2857, \frac{101}{84} \approx 1.202
\]

### Third Column
\[
\frac{1}{5}, \frac{2}{7}, \frac{3}{5}, \text{?}
\]

### Fourth Column
\[
\frac{19}{20}, \frac{19}{21}, \text{?}, \frac{507}{140}
\]

From here, let's use logic and inference for our missing fractions.

### Solving for missing fractions:

1. **First Column**: From \(\frac{1}{2}\), \(\frac{2}{4}\), \(\frac{4}{3}\), it seems an incremental multiplication sequence might fit. 
   - Hypothetically for \(? = \frac{1 \cdot 2}{2} = 1\)

2. **Second Column**: Similarly, second missing would be approximated:
   - Consider \(101/84 \approx 1.202\)

3. **Third Column**: Looks like logical arithmetic:
   - \(1/5, 2/7, 3/5\)

4. **Fourth Column**: 

For easy verification, it results in \(? = 0.2857\)

Thus, reapplying:

\[
\begin{array}{|c|c|c|c|}
\hline
\frac{1}{2} & \frac{1}{4} & \frac{1}{5} & \frac{19}{20} \\
\hline
1 & \frac{2}{7} & \frac{2}{7} & \frac{19}{21} \\
\hline
\frac{2}{4} & 1 & \frac{3}{5} & \frac{19}{21} \\
\hline
\frac{4}{3} & \frac{101}{84} & \frac{19}{21} & \frac{507}{140} \\
\hline
\end{array}
\]

Would you like detailed explanation or more specific pattern analysis?
### Questions you can ask:
1. How to verify a pattern of fraction sequences?
2. Can you explain how to check progression in fraction sequences?
3. How do identify and cross-verify fractions?
4. What are steps to simplify fractions easily?
5. How to solve fractions and sequences accurately?

### Tip:
Always cross-verify missing values in sequence progression using common arithmetic or geometric progressions to ensure accuracy.

Learn how to analyze and solve complex fraction sequences using arithmetic and geometric progressions. This detailed solution covers the identification of patterns in fraction sequences and logical inference to find missing values. Suitable for high school students studying fractions and sequences.

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