Find any five rational numbers between 1 by 10 and 1 by 5

To find five rational numbers between \(\frac{1}{10}\) and \(\frac{1}{5}\), we can use the method of finding equivalent fractions with a common denominator.

First, let's convert both fractions to have a common denominator:

\[
\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}
\]
\[
\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
\]

Now we need to find five rational numbers between \(\frac{2}{20}\) and \(\frac{4}{20}\). The fractions between these two can be determined by looking at the fractions with the same denominator (20) and numerators between 2 and 4. Here are some possible fractions:

\[
\frac{3}{20}
\]

However, to find more than one, we need to find fractions equivalent to some common fractions or use larger denominators. We can use fractions with denominators that are multiples of 20. Here are five such rational numbers:

1. \(\frac{5}{40}\) (simplifies to \(\frac{1}{8}\))
2. \(\frac{7}{40}\)
3. \(\frac{9}{40}\)
4. \(\frac{3}{20}\) (already identified)
5. \(\frac{11}{40}\)

Thus, five rational numbers between \(\frac{1}{10}\) and \(\frac{1}{5}\) are:

1. \(\frac{5}{40} = \frac{1}{8}\)
2. \(\frac{7}{40}\)
3. \(\frac{9}{40}\)
4. \(\frac{3}{20}\)
5. \(\frac{11}{40}\)

Would you like more details or have any questions about these rational numbers?

Here are 8 additional questions to expand on this topic:
1. How do you convert a fraction to an equivalent fraction with a different denominator?
2. What is the process for finding a common denominator between two fractions?
3. How do you simplify a fraction?
4. What are rational numbers and how are they different from irrational numbers?
5. Can you find rational numbers between other fractions, like \(\frac{1}{3}\) and \(\frac{1}{2}\)?
6. How would you find rational numbers between two fractions with different denominators?
7. Why is it useful to understand how to find equivalent fractions?
8. How can finding rational numbers between two fractions help in real-world applications?

**Tip:** When working with fractions, always try to simplify them to their lowest terms to make calculations easier and more intuitive.

Learn how to find five rational numbers between \(\frac{1}{10}\) and \(\frac{1}{5}\) using equivalent fractions and common denominators. This problem covers key concepts in fractions and rational numbers, suitable for Grades 5-6.

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