Let's analyze each statement to determine its validity step-by-step.
1. Statement 1: [tex]\(\frac{3}{4} < \frac{2}{3}\)[/tex]
To compare these two fractions, we need to find a common denominator or convert them into decimal form:
[tex]\[\frac{3}{4} = 0.75\][/tex]
[tex]\[\frac{2}{3} \approx 0.6667\][/tex]
Clearly, [tex]\(0.75\)[/tex] is greater than [tex]\(0.6667\)[/tex], so:
[tex]\[
\frac{3}{4} > \frac{2}{3}
\][/tex]
This statement is false.
2. Statement 2: [tex]\(\frac{9}{15} < \frac{4}{5}\)[/tex]
Let's compare [tex]\(\frac{9}{15}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex] by simplifying [tex]\(\frac{9}{15}\)[/tex] first:
[tex]\[\frac{9}{15} = \frac{3 \times 3}{3 \times 5} = \frac{3}{5}\][/tex]
Next, convert both fractions into decimal form for a clearer comparison:
[tex]\[\frac{3}{5} = 0.6\][/tex]
[tex]\[\frac{4}{5} = 0.8\][/tex]
Clearly, [tex]\(0.6\)[/tex] is less than [tex]\(0.8\)[/tex], so:
[tex]\[
\frac{9}{15} < \frac{4}{5}
\][/tex]
This statement is true.
3. Statement 3: [tex]\(\frac{18}{27} = \frac{1}{3}\)[/tex]
To verify if these fractions are equal, we can simplify [tex]\(\frac{18}{27}\)[/tex]:
[tex]\[\frac{18}{27} = \frac{18 \div 9}{27 \div 9} = \frac{2}{3}\][/tex]
Now, comparing [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[\frac{2}{3} \neq \frac{1}{3}\][/tex]
This statement is false.
4. Statement 4: [tex]\(\frac{5}{6} > \frac{11}{12}\)[/tex]
To compare these fractions, convert them into decimal form:
[tex]\[\frac{5}{6} \approx 0.8333\][/tex]
[tex]\[\frac{11}{12} \approx 0.9167\][/tex]
Clearly, [tex]\(0.8333\)[/tex] is less than [tex]\(0.9167\)[/tex], so:
[tex]\[
\frac{5}{6} < \frac{11}{12}
\][/tex]
This statement is false.
After evaluating all the statements, the only true statement is:
[tex]\[
\frac{9}{15} < \frac{4}{5}
\][/tex]
