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Calculate the result of the expression:

[tex]\[ 2.35 \cdot \frac{2}{3} \][/tex]

Choose the correct answer from the options below:

A. [tex]\(\frac{7}{30}\)[/tex]

B. [tex]\(\frac{7}{15}\)[/tex]

C. [tex]\(\frac{27}{30}\)[/tex]

D. [tex]\(\frac{47}{30}\)[/tex]

Answer :

To solve the problem, we start by converting the decimal [tex]$2.35$[/tex] into a fraction. Notice that:

[tex]$$
2.35 = \frac{235}{100}
$$[/tex]

This fraction can be simplified. Both the numerator and the denominator are divisible by [tex]$5$[/tex]:

[tex]$$
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
$$[/tex]

Now we multiply this fraction by [tex]$\frac{2}{3}$[/tex]:

[tex]$$
\frac{47}{20} \times \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
$$[/tex]

The fraction [tex]$\frac{94}{60}$[/tex] can be simplified by dividing both the numerator and the denominator by [tex]$2$[/tex]:

[tex]$$
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
$$[/tex]

Thus, the final answer is:

[tex]$$
\frac{47}{30}
$$[/tex]

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