Let's compare the fractions [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex].
1. Express the fractions with a common denominator
- The common denominator for 2 and 4 is 4.
- Convert [tex]\( \frac{1}{2} \)[/tex] to an equivalent fraction with a denominator of 4:
[tex]\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\][/tex]
- Now, we have the fractions [tex]\( \frac{2}{4} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex].
2. Compare the numerators:
- The fraction [tex]\( \frac{2}{4} \)[/tex] has a numerator of 2.
- The fraction [tex]\( \frac{3}{4} \)[/tex] has a numerator of 3.
- Since 2 is less than 3, we can say that:
[tex]\[
\frac{2}{4} < \frac{3}{4}
\][/tex]
3. Conclusion:
- Therefore, [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex].
So, the best answer is:
B. [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex]
