Let's compare the two fractions [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex] step by step:
1. First, let's understand 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. To compare the fractions, we can find a common denominator. The denominators of the given fractions are 2 and 4. The least common multiple (LCM) of 2 and 4 is 4.
3. Convert [tex]\( \frac{1}{2} \)[/tex] to an equivalent fraction with the denominator 4:
- [tex]\( \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \)[/tex]
4. Now we can compare [tex]\( \frac{2}{4} \)[/tex] with [tex]\( \frac{3}{4} \)[/tex]:
- [tex]\( \frac{2}{4} \)[/tex] is clearly less than [tex]\( \frac{3}{4} \)[/tex] since 2 is less than 3.
5. Therefore, [tex]\( \frac{1}{2} \)[/tex] is less than [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{1}{2} < \frac{3}{4}
\][/tex]
Hence, the correct answer is:
A. [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex]
