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Simplify the expression:

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

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 :

Sure, let's solve [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] step-by-step.

1. First, break down the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex].

2. Multiply the decimal number by the fraction:
[tex]\[
2.35 \cdot \frac{2}{3}
\][/tex]

3. To make it easier, let's first convert [tex]\(2.35\)[/tex] into a fraction:
[tex]\[
2.35 = \frac{235}{100}
\][/tex]
So the multiplication becomes:
[tex]\[
\frac{235}{100} \cdot \frac{2}{3}
\][/tex]

4. Next, multiply the numerators and denominators:
[tex]\[
\frac{235 \cdot 2}{100 \cdot 3} = \frac{470}{300}
\][/tex]

5. Simplify the fraction [tex]\(\frac{470}{300}\)[/tex]:
[tex]\[
\text{The GCD of 470 and 300 is 10, so divide both the numerator and denominator by 10:}
\][/tex]
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]

So, [tex]\(2.35 \cdot \frac{2}{3}= \frac{47}{30}\)[/tex].

Therefore, the correct answer is
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]

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