To find 5 ratios (or fractions) between $\frac{1}{2}$ and $\frac{3}{5}$, we can express these fractions with a common denominator and then generate fractions in between.

1. Start by converting $\frac{1}{2}$ and $\frac{3}{5}$ to have a common denominator: $\frac{1}{2} = \frac{5}{10}, \quad \frac{3}{5} = \frac{6}{10}.$

2. Now, we look for 5 fractions between $\frac{5}{10}$ and $\frac{6}{10}$. One way to do this is to scale up the denominators to allow for more "space" between these two numbers.

Let's scale both fractions by 10: $\frac{5}{10} = \frac{50}{100}, \quad \frac{6}{10} = \frac{60}{100}.$

3. Now, we can pick 5 fractions between $\frac{50}{100}$ and $\frac{60}{100}$:

• $\frac{51}{100}$
• $\frac{52}{100}$
• $\frac{53}{100}$
• $\frac{54}{100}$
• $\frac{55}{100}$

These are all fractions between $\frac{1}{2}$ and $\frac{3}{5}$ in simplest form.

Would you like further details on this process or have any other questions?

Here are 5 related questions to explore:

1. How can you simplify fractions like $\frac{51}{100}$?
2. How do you find the least common denominator between two fractions?
3. What is the process for comparing fractions with different denominators?
4. How can you find fractions between any two given fractions?
5. How do you convert a fraction to a decimal and vice versa?

Tip: When comparing fractions, converting them to have the same denominator makes it much easier to see which one is larger or smaller.