To determine which of the given statements is true, we need to compare the fractions accurately. Here are the detailed steps for each comparison:
1. Compare [tex]\(\frac{6}{16}\)[/tex] and [tex]\(\frac{5}{10}\)[/tex]:
Simplify each fraction:
[tex]\[
\frac{6}{16} = \frac{3}{8}
\][/tex]
[tex]\[
\frac{5}{10} = \frac{1}{2}
\][/tex]
Compare:
[tex]\[
\frac{3}{8} < \frac{1}{2}
\][/tex]
Therefore, [tex]\(\frac{6}{16} < \frac{5}{10}\)[/tex] is true, so [tex]\(\frac{6}{16} > \(\frac{5}{10}\)[/tex] is false.
2. Compare [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{6}{16}\)[/tex]:
Simplify [tex]\(\frac{6}{16}\)[/tex]:
[tex]\[
\frac{6}{16} = \frac{3}{8}
\][/tex]
Compare:
[tex]\[
\frac{3}{5} > \frac{3}{8}
\][/tex]
Therefore, [tex]\(\(\frac{3}{5} < \frac{6}{16}\)[/tex] is false.
3. Compare [tex]\(\frac{4}{8}\)[/tex] and [tex]\(\frac{6}{16}\)[/tex]:
Simplify both fractions:
[tex]\[
\frac{4}{8} = \frac{1}{2}
\][/tex]
[tex]\[
\frac{6}{16} = \frac{3}{8}
\][/tex]
Compare:
[tex]\[
\frac{1}{2} > \frac{3}{8}
\][/tex]
Therefore, [tex]\(\(\frac{4}{8} < \frac{6}{16}\)[/tex] is false.
4. Compare [tex]\(\frac{6}{16}\)[/tex] and [tex]\(\frac{8}{24}\)[/tex]:
Simplify both fractions:
[tex]\[
\frac{6}{16} = \frac{3}{8}
\][/tex]
[tex]\[
\frac{8}{24} = \frac{1}{3}
\][/tex]
Compare:
[tex]\[
\frac{3}{8} > \frac{1}{3}
\][/tex]
Therefore, [tex]\(\(\frac{6}{16} > \frac{8}{24}\)[/tex] is true.
So, the true statement is:
[tex]\[
\(\frac{6}{16} > \frac{8}{24}\)
\][/tex]
The correct answer is the fourth statement, which means the true statement is:
[tex]\(\frac{6}{16} > \frac{8}{24}\)[/tex].
