To determine which of the given statements is true, we'll analyze each one step by step.
### Statement 1: [tex]\(\frac{5}{6} > \frac{10}{12}\)[/tex]
First, let's simplify [tex]\(\frac{10}{12}\)[/tex]:
[tex]\[
\frac{10}{12} = \frac{10 \div 2}{12 \div 2} = \frac{5}{6}
\][/tex]
Now we compare [tex]\(\frac{5}{6}\)[/tex] with [tex]\(\frac{5}{6}\)[/tex]:
[tex]\[
\frac{5}{6} = \frac{5}{6}
\][/tex]
Hence,
[tex]\[
\frac{5}{6} > \frac{10}{12} \quad \text{is false}
\][/tex]
### Statement 2: [tex]\(\frac{8}{16} = \frac{1}{4}\)[/tex]
Next, let's simplify [tex]\(\frac{8}{16}\)[/tex]:
[tex]\[
\frac{8}{16} = \frac{8 \div 8}{16 \div 8} = \frac{1}{2} \quad \text{(not } \frac{1}{4}\text{)}
\][/tex]
Therefore,
[tex]\[
\frac{8}{16} = \frac{1}{4} \quad \text{is false}
\][/tex]
### Statement 3: [tex]\(\frac{3}{4} < \frac{4}{6}\)[/tex]
Next, let's simplify [tex]\(\frac{4}{6}\)[/tex]:
[tex]\[
\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\][/tex]
Now we compare [tex]\(\frac{3}{4}\)[/tex] with [tex]\(\frac{2}{3}\)[/tex]:
First, convert them to common denominators or decimals:
[tex]\[
\frac{3}{4} = 0.75 \quad \text{and} \quad \frac{2}{3} \approx 0.6667
\][/tex]
Since [tex]\(0.75\)[/tex] is greater than [tex]\(0.6667\)[/tex],
[tex]\[
\frac{3}{4} < \frac{4}{6} \quad \text{is false}
\][/tex]
### Statement 4: [tex]\(\frac{11}{15} < \frac{4}{5}\)[/tex]
Let's express [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{11}{15}\)[/tex] with a common denominator, [tex]\(15\)[/tex]:
[tex]\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\][/tex]
Now we compare [tex]\(\frac{11}{15}\)[/tex] with [tex]\(\frac{12}{15}\)[/tex]:
[tex]\[
\frac{11}{15} < \frac{12}{15}
\][/tex]
This is true.
### Conclusion
Out of all the provided comparisons, the true statement is:
[tex]\[
\frac{11}{15} < \frac{4}{5}
\][/tex]
