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Calculate the product:

[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 :

To solve the problem, we want to multiply [tex]\(2.35\)[/tex] by [tex]\(\frac{2}{3}\)[/tex] and find the answer as a fraction.

1. Convert [tex]\(2.35\)[/tex] to a Fraction:
- First, express [tex]\(2.35\)[/tex] as a fraction. To do this, note that [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex] because it is the same as 235 hundredths.

2. Simplify the Fraction:
- Simplify [tex]\(\frac{235}{100}\)[/tex]. Divide both the numerator and the denominator by their greatest common divisor, which is 5.
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]

3. Multiply the Fractions:
- Now, multiply the simplified fraction [tex]\(\frac{47}{20}\)[/tex] 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]

4. Simplify the Resulting Fraction:
- Simplify [tex]\(\frac{94}{60}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[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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