Let's review each of the given inequalities one by one to determine which inequality is true.
A. [tex]\(\frac{3}{4} < \frac{5}{7}\)[/tex]
To compare these fractions, we can calculate their decimal equivalents:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
- [tex]\(\frac{5}{7} \approx 0.714\)[/tex]
So, [tex]\(0.75\)[/tex] is not less than [tex]\(0.714\)[/tex], hence [tex]\(\frac{3}{4} < \frac{5}{7}\)[/tex] is false.
B. [tex]\(\frac{2}{3} > \frac{5}{6}\)[/tex]
By calculating the decimal equivalents:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{5}{6} \approx 0.8333\)[/tex]
Here, [tex]\(0.6667\)[/tex] is not greater than [tex]\(0.8333\)[/tex], hence [tex]\(\frac{2}{3} > \frac{5}{6}\)[/tex] is false.
C. [tex]\(\frac{5}{8} > \frac{6}{10}\)[/tex]
Calculating the decimal equivalents for these fractions:
- [tex]\(\frac{5}{8} = 0.625\)[/tex]
- [tex]\(\frac{6}{10} = 0.6\)[/tex]
Since [tex]\(0.625\)[/tex] is indeed greater than [tex]\(0.6\)[/tex], [tex]\(\frac{5}{8} > \frac{6}{10}\)[/tex] is true.
D. [tex]\(\frac{4}{5} < \frac{2}{9}\)[/tex]
Calculating their decimal equivalents:
- [tex]\(\frac{4}{5} = 0.8\)[/tex]
- [tex]\(\frac{2}{9} \approx 0.222\)[/tex]
Here, [tex]\(0.8\)[/tex] is not less than [tex]\(0.222\)[/tex], hence [tex]\(\frac{4}{5} < \frac{2}{9}\)[/tex] is false.
Given this analysis, the correct inequality, and the one that is true, is:
C. [tex]\(\frac{5}{8} > \frac{6}{10}\)[/tex]
