To find four rational numbers between $\frac{1}{5}$ and $\frac{1}{4}$, we can follow these steps:

1. Convert the fractions to have a common denominator:

   The denominators of $\frac{1}{5}$ and $\frac{1}{4}$ are 5 and 4, respectively. The least common denominator (LCD) of 5 and 4 is 20.

   Convert $\frac{1}{5}$ and $\frac{1}{4}$ to fractions with a denominator of 20: $\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$ $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$

2. Find four rational numbers between $\frac{4}{20}$ and $\frac{5}{20}$:

   To find four rational numbers between $\frac{4}{20}$ and $\frac{5}{20}$, we can create fractions with a higher common denominator.

   Let's increase the denominator to 40: $\frac{4}{20} = \frac{4 \times 2}{20 \times 2} = \frac{8}{40}$ $\frac{5}{20} = \frac{5 \times 2}{20 \times 2} = \frac{10}{40}$

   Now we can find rational numbers between $\frac{8}{40}$ and $\frac{10}{40}$: $\frac{9}{40}$

   To find more, let's use a higher denominator, say 60: $\frac{4}{20} = \frac{4 \times 3}{20 \times 3} = \frac{12}{60}$ $\frac{1}{4} = \frac{1 \times 15}{4 \times 15} = \frac{15}{60}$

   Now we can find rational numbers between $\frac{12}{60}$ and $\frac{15}{60}$: $\frac{13}{60}, \frac{14}{60}$

   Using a higher denominator, 80: $\frac{4}{20} = \frac{4 \times 4}{20 \times 4} = \frac{16}{80}$ $\frac{1}{4} = \frac{1 \times 20}{4 \times 20} = \frac{20}{80}$

   Now we can find rational numbers between $\frac{16}{80}$ and $\frac{20}{80}$: $\frac{17}{80}, \frac{18}{80}, \frac{19}{80}$

Combining all the found rational numbers, we get:

• $\frac{9}{40}$
• $\frac{13}{60}$
• $\frac{14}{60}$
• $\frac{17}{80}$
• $\frac{18}{80}$
• $\frac{19}{80}$

So, four rational numbers between $\frac{1}{5}$ and $\frac{1}{4}$ are:

1. $\frac{9}{40}$
2. $\frac{13}{60}$
3. $\frac{14}{60}$
4. $\frac{17}{80}$

Would you like more details on the process or have any questions?

Here are some related questions:

1. How do you find the least common denominator of two fractions?
2. What are rational numbers and how do they differ from irrational numbers?
3. How can you determine if a number is rational or irrational?
4. How can you convert a mixed number to an improper fraction?
5. What is the process to add or subtract fractions with different denominators?
6. How can you simplify a fraction?
7. What are some examples of rational numbers between 0 and 1?
8. How do you convert a repeating decimal to a fraction?

Tip: When finding numbers between two fractions, converting them to have a common denominator makes it easier to identify intermediate values.