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To solve this problem, we need to compare the fractions \( \frac{16}{100}, \frac{9}{50}, \frac{1}{4} \) and check the options to determine which set is arranged in ascending order.

### Step 1: Convert fractions to a common denominator
To compare fractions, it is easier to convert them to a common denominator. The least common denominator (LCD) of 100, 50, and 4 is 100.

1. \( \frac{16}{100} \) is already in terms of 100.
2. Convert \( \frac{9}{50} \) to a denominator of 100:
   \[
   \frac{9}{50} = \frac{9 \times 2}{50 \times 2} = \frac{18}{100}
   \]
3. Convert \( \frac{1}{4} \) to a denominator of 100:
   \[
   \frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}
   \]

### Step 2: Compare the fractions
Now we compare the fractions with a denominator of 100:
- \( \frac{16}{100} = 16\)
- \( \frac{9}{50} = \frac{18}{100} \)
- \( \frac{1}{4} = \frac{25}{100} \)

In ascending order, these fractions are:
\[
\frac{16}{100} < \frac{18}{100} < \frac{25}{100}
\]
Which means:
\[
\frac{16}{100} < \frac{9}{50} < \frac{1}{4}
\]

### Step 3: Analyze the given options
- **Option (A):** \( \frac{16}{100} < \frac{9}{50} < \frac{1}{4} \) — This is correct.
- **Option (B):** \( \frac{1}{4} < \frac{9}{50} < \frac{16}{100} \) — This is incorrect.
- **Option (C):** \( \frac{1}{4} < \frac{16}{100} < \frac{9}{50} \) — This is incorrect.

### Final Answer:
The correct answer is **(A)**.

Would you like more details on the explanation or another related example?

Here are some related questions to expand on this:

1. How do you find the least common denominator for fractions?
2. What is the process for converting fractions to equivalent fractions with the same denominator?
3. How can you compare fractions without converting them to the same denominator?
4. How would this method change if dealing with improper fractions?
5. What role do decimals play in comparing fractions?

**Tip:** Converting fractions to decimals is another quick way to compare their values.

In which of the following option fractions are correctly arranged in ascending order (smallest to greatest)? 16/100, 9/50, 1/4

This problem demonstrates how to arrange the fractions 16/100, 9/50, and 1/4 in ascending order. It involves finding a common denominator and comparing the values. Suitable for students in Grades 6-8, this solution walks through the step-by-step process of fraction comparison.

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