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1. Put these fractions in order from smallest to largest:
[tex]\[ \frac{4}{5}, \frac{3}{4}, \frac{9}{10}, \frac{17}{20}, \frac{3}{5} \][/tex]

A. [tex]\[ \frac{4}{5}, \frac{3}{4}, \frac{3}{5}, \frac{17}{20}, \frac{9}{10} \][/tex]

B. [tex]\[ \frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{9}{10}, \frac{17}{20} \][/tex]

C. [tex]\[ \frac{3}{4}, \frac{3}{5}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10} \][/tex]

D. [tex]\[ \frac{3}{5}, \frac{3}{4}, \frac{4}{5}, \frac{17}{20}, \frac{9}{10} \][/tex]


Sagot :

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]