To solve the problem step-by-step, let's consider the expression [tex]\(2.35 \cdot \frac{2}{3}\)[/tex]:
1. Convert 2.35 to a fraction.
[tex]\[
2.35 = \frac{235}{100}
\][/tex]
2. Multiply the fraction by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{235}{100} \cdot \frac{2}{3} = \frac{235 \cdot 2}{100 \cdot 3} = \frac{470}{300}
\][/tex]
3. Simplify the fraction [tex]\(\frac{470}{300}\)[/tex]:
- Find the greatest common divisor (GCD) of 470 and 300:
- The GCD of 470 and 300 is 10.
- Divide both the numerator and the denominator by their GCD (10):
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Thus, the simplified form of the expression [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
Among the given options:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
The correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
