To determine which symbol correctly compares the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], we need to evaluate their values and see how they stand in relation to each other.
Step-by-Step Solution:
1. Understand and Convert the Fractions:
- [tex]\(\frac{1}{2}\)[/tex] represents one part out of two equal parts.
- [tex]\(\frac{3}{4}\)[/tex] represents three parts out of four equal parts.
2. Compare the Fractions:
- We want to determine if [tex]\(\frac{1}{2}\)[/tex] is greater than, less than, or equal to [tex]\(\frac{3}{4}\)[/tex].
3. Using a Common Denominator (Optional):
- Convert both fractions to a common denominator to easily compare them. The denominators here are 2 and 4. The least common denominator is 4.
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{2}{4}\)[/tex]. Now we have:
[tex]\[
\frac{2}{4} \quad \text{and} \quad \frac{3}{4}
\][/tex]
4. Direct Comparison:
- Compare the numerators with the same denominator:
[tex]\[
2 \quad \text{and} \quad 3
\][/tex]
- Since [tex]\(2 < 3\)[/tex], we can conclude that:
[tex]\[
\frac{2}{4} < \frac{3}{4}
\][/tex]
Thus, [tex]\(\frac{1}{2} < \frac{3}{4}\)[/tex].
Conclusion:
The correct answer is:
[tex]\[
\boxed{<}
\][/tex]
Therefore, the correct comparison symbol for the given fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\boxed{B} \, <\)[/tex].
