​ find for rational number between 1 / 5 and 1/4

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.

Discover how to find four rational numbers between 1/5 and 1/4 with a detailed step-by-step solution. This problem covers fractions and number theory concepts. Suitable for Grades 5-7.

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