To compare the fractions [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex], let's break down the process:
1. Convert the fractions to decimals:
- [tex]\( \frac{1}{2} \)[/tex] can be converted to its decimal form by dividing the numerator by the denominator:
[tex]\[
\frac{1}{2} = 0.5
\][/tex]
- [tex]\( \frac{3}{4} \)[/tex] can be converted to its decimal form similarly:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
2. Compare the decimal forms:
- We now compare the decimal values [tex]\( 0.5 \)[/tex] and [tex]\( 0.75 \)[/tex].
- Since [tex]\( 0.5 \)[/tex] is less than [tex]\( 0.75 \)[/tex], we conclude that:
[tex]\[
0.5 < 0.75
\][/tex]
3. Translate this back to the fraction comparison:
- Since [tex]\( 0.5 \)[/tex] corresponds to [tex]\( \frac{1}{2} \)[/tex] and [tex]\( 0.75 \)[/tex] corresponds to [tex]\( \frac{3}{4} \)[/tex], we have:
[tex]\[
\frac{1}{2} < \frac{3}{4}
\][/tex]
Thus, the best answer is:
B. [tex]\( \frac{1}{2} < \frac{3}{4} \)[/tex]
