https://file.aiquickdraw.com/mathbot/file/1727317701456svjr9xl2.jpg

Let's break down each of the three parts from the image and explore potential solutions.

### (1) Using digits 0, 1, 2, 3, 5, and 6, form the fraction and percentage
You need to create a fraction \( \frac{ab}{cd} \) where \( a, b, c, d \) are digits that form two-digit numbers, and the fraction equals a percentage. For example, one solution might be \( \frac{65}{100} = 65\% \). You need 8 different combinations, so here are some potential ones:

- \( \frac{50}{100} = 50\% \)
- \( \frac{36}{72} = 50\% \)
- \( \frac{15}{30} = 50\% \)
- \( \frac{12}{24} = 50\% \)
- \( \frac{25}{50} = 50\% \)
- \( \frac{10}{20} = 50\% \)
- \( \frac{60}{120} = 50\% \)
- \( \frac{30}{60} = 50\% \)

### (2) Using digits 3, 4, 5, 6, 7, and 8 to form a fraction and percentage
This is similar to the previous one, but using the digits provided. You need 4 combinations. For instance:

- \( \frac{75}{150} = 50\% \)
- \( \frac{48}{96} = 50\% \)
- \( \frac{36}{72} = 50\% \)
- \( \frac{24}{48} = 50\% \)

### (3) Forming the largest and smallest percentages less than 100%
You can experiment with various combinations of digits to achieve both the largest and smallest percentages.

**Largest percentage (less than 100%):**
- \( \frac{98}{99} \approx 99\% \)

**Smallest percentage (greater than 0%):**
- \( \frac{1}{99} \approx 1\% \)

Would you like more specific or additional solutions for each of these parts? 

### 5 Related Questions:
1. How would you adjust the approach if 3-digit numbers were allowed?
2. Can you find other pairs of digits to produce percentages close to 25% or 75%?
3. What is the effect of increasing or decreasing the denominator on the percentage value?
4. How could this task be generalized to larger numbers or different sets of digits?
5. How could this exercise help reinforce the concept of equivalent fractions?

### Tip:
When dealing with fractions and percentages, always simplify the fraction first, if possible, to make calculations easier.

Different ways to represent a/b as a percentage using the digits 0, 1, 2, 3, 5, 6 for one fraction and the digits 3, 4, 5, 6, 7, 8 for another fraction.

Explore how to express fractions as percentages using specific digits (0, 1, 2, 3, 5, 6 and 3, 4, 5, 6, 7, 8). Find different solutions to make fractions equal percentages. Suitable for Grades 5-7, this problem reinforces key concepts in fractions and percentages.

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