To solve the problem of ordering the fractions [tex]\(\frac{4}{5}, \frac{3}{4}, \frac{9}{10}, \frac{17}{20}, \frac{3}{5}\)[/tex] from smallest to largest, follow these steps:
1. Convert each fraction to its decimal form to facilitate comparison:
- [tex]\(\frac{4}{5} = 0.8\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{9}{10} = 0.9\)[/tex]
- [tex]\(\frac{17}{20} = 0.85\)[/tex]
- [tex]\(\frac{3}{5} = 0.6\)[/tex]
2. List these decimal values:
- [tex]\(0.8, 0.75, 0.9, 0.85, 0.6\)[/tex]
3. Sort these decimal values in ascending order:
- [tex]\(0.6, 0.75, 0.8, 0.85, 0.9\)[/tex]
4. Match these sorted decimal values back to their respective fractions:
- [tex]\(0.6 \rightarrow \frac{3}{5}\)[/tex]
- [tex]\(0.75 \rightarrow \frac{3}{4}\)[/tex]
- [tex]\(0.8 \rightarrow \frac{4}{5}\)[/tex]
- [tex]\(0.85 \rightarrow \frac{17}{20}\)[/tex]
- [tex]\(0.9 \rightarrow \frac{9}{10}\)[/tex]
5. Write the fractions in their new order from smallest to largest:
- [tex]\(\frac{3}{5}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{4}{5}\)[/tex]
- [tex]\(\frac{17}{20}\)[/tex]
- [tex]\(\frac{9}{10}\)[/tex]
Comparing the provided choices:
1. [tex]\(\frac{4}{5}, \frac{3}{4}, \frac{3}{5}, \frac{17}{20}, \frac{9}{10}\)[/tex]
2. [tex]\(\frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{9}{10}, \frac{17}{20}\)[/tex]
3. [tex]\(\frac{3}{4}, \frac{3}{5}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10}\)[/tex]
4. [tex]\(\frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10}\)[/tex]
The correct answer is:
[tex]\(\boxed{\frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10}}\)[/tex]
