To compare the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{6}{9} \)[/tex], we can break the solution down step-by-step.
1. Simplify the fractions (if necessary):
- [tex]\( \frac{2}{3} \)[/tex] is already in its simplest form.
- To check if [tex]\( \frac{6}{9} \)[/tex] is in its simplest form, find the greatest common divisor (GCD) of 6 and 9, which is 3. Simplifying [tex]\( \frac{6}{9} \)[/tex]:
[tex]\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\][/tex]
2. Convert each fraction to a decimal:
- [tex]\( \frac{2}{3} \)[/tex] as a decimal is [tex]\( 0.666\ldots \)[/tex] (recurring).
- Since we simplified [tex]\( \frac{6}{9} \)[/tex] to [tex]\( \frac{2}{3} \)[/tex], its decimal form is also [tex]\( 0.666\ldots \)[/tex] (recurring).
3. Compare the decimal values:
- We have [tex]\( 0.666\ldots \)[/tex] for both fractions.
4. Determine the correct comparison symbol:
- Since the decimal values [tex]\( 0.666\ldots \)[/tex] are the same, [tex]\( \frac{2}{3} \)[/tex] is equal to [tex]\( \frac{6}{9} \)[/tex].
Therefore, the correct symbol to compare [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{6}{9} \)[/tex] is [tex]\( = \)[/tex].
The answer is C. [tex]\( = \)[/tex]
