Find trusted answers to your questions with the help of IDNLearn.com's knowledgeable community. Get the information you need from our community of experts, who provide detailed and trustworthy answers.

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]