To compare the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex], let's analyze their values in a step-by-step manner.
Step 1: Convert the fractions to decimal form
- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex] (since [tex]\( 2 \div 3 = 0.6667 \)[/tex])
- [tex]\( \frac{3}{4} = 0.75 \)[/tex] (since [tex]\( 3 \div 4 = 0.75 \)[/tex])
Step 2: Compare the decimal values
Given the decimal equivalents:
- [tex]\( 0.6667 \)[/tex] (which represents [tex]\( \frac{2}{3} \)[/tex])
- [tex]\( 0.75 \)[/tex] (which represents [tex]\( \frac{3}{4} \)[/tex])
Clearly, [tex]\( 0.6667 < 0.75 \)[/tex].
Step 3: Draw the conclusion
Since [tex]\( 0.6667 < 0.75 \)[/tex], we can conclude that:
[tex]\[ \frac{2}{3} < \frac{3}{4} \][/tex]
Therefore, the correct answer is:
A. [tex]\( \frac{2}{3} < \frac{3}{4} \)[/tex]
