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Calculate the product of [tex]2.35 \cdot \frac{2}{3}[/tex] and choose the correct result.

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 :

We start by converting the decimal [tex]$2.35$[/tex] into a fraction:

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

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

[tex]$$
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
$$[/tex]

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is [tex]$10$[/tex]:

[tex]$$
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
$$[/tex]

Thus, the final simplified answer is:

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

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