Answer :
To determine which set of fractions is ordered from least to greatest, we need to compare the given fractions: [tex]\(\frac{5}{8}\)[/tex], [tex]\(\frac{8}{12}\)[/tex], and [tex]\(\frac{3}{4}\)[/tex].
Step-by-step:
1. Convert each fraction to its decimal form for easier comparison:
- [tex]\(\frac{5}{8} = 0.625\)[/tex]
- [tex]\(\frac{8}{12} = \frac{2}{3} \approx 0.666\overline{6}\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
2. Sort the decimal values from least to greatest:
- [tex]\(0.625\)[/tex] (the decimal value for [tex]\(\frac{5}{8}\)[/tex])
- [tex]\(0.666\overline{6}\)[/tex] (the decimal value for [tex]\(\frac{8}{12}\)[/tex])
- [tex]\(0.75\)[/tex] (the decimal value for [tex]\(\frac{3}{4}\)[/tex])
3. Match the sorted decimal values back to their respective fractions:
- [tex]\(0.625\)[/tex] corresponds to [tex]\(\frac{5}{8}\)[/tex]
- [tex]\(0.666\overline{6}\)[/tex] corresponds to [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(0.75\)[/tex] corresponds to [tex]\(\frac{3}{4}\)[/tex]
4. List the fractions in order from least to greatest based on their decimal equivalents:
- [tex]\(\frac{5}{8}\)[/tex]
- [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
Therefore, the set of fractions ordered from least to greatest is:
[tex]\[ \boxed{\frac{5}{8}, \frac{8}{12}, \frac{3}{4}} \][/tex]
This matches with option A:
[tex]\[ A: \frac{5}{8}, \frac{8}{12}, \frac{3}{4} \][/tex]
Step-by-step:
1. Convert each fraction to its decimal form for easier comparison:
- [tex]\(\frac{5}{8} = 0.625\)[/tex]
- [tex]\(\frac{8}{12} = \frac{2}{3} \approx 0.666\overline{6}\)[/tex]
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
2. Sort the decimal values from least to greatest:
- [tex]\(0.625\)[/tex] (the decimal value for [tex]\(\frac{5}{8}\)[/tex])
- [tex]\(0.666\overline{6}\)[/tex] (the decimal value for [tex]\(\frac{8}{12}\)[/tex])
- [tex]\(0.75\)[/tex] (the decimal value for [tex]\(\frac{3}{4}\)[/tex])
3. Match the sorted decimal values back to their respective fractions:
- [tex]\(0.625\)[/tex] corresponds to [tex]\(\frac{5}{8}\)[/tex]
- [tex]\(0.666\overline{6}\)[/tex] corresponds to [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(0.75\)[/tex] corresponds to [tex]\(\frac{3}{4}\)[/tex]
4. List the fractions in order from least to greatest based on their decimal equivalents:
- [tex]\(\frac{5}{8}\)[/tex]
- [tex]\(\frac{8}{12}\)[/tex]
- [tex]\(\frac{3}{4}\)[/tex]
Therefore, the set of fractions ordered from least to greatest is:
[tex]\[ \boxed{\frac{5}{8}, \frac{8}{12}, \frac{3}{4}} \][/tex]
This matches with option A:
[tex]\[ A: \frac{5}{8}, \frac{8}{12}, \frac{3}{4} \][/tex]
