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Calculate the following:

[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 question [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we need to multiply the decimal number by the fraction. Here's how you can do it step by step:

1. Convert the Decimal to a Fraction:
Start with the decimal [tex]\(2.35\)[/tex]. This can be expressed as a fraction:
[tex]\[
2.35 = \frac{235}{100}
\][/tex]

2. Multiply the Two Fractions:
Next, multiply [tex]\(\frac{235}{100}\)[/tex] 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]

3. Simplify the Fraction:
To simplify [tex]\(\frac{470}{300}\)[/tex], divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD is 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]

So, the final answer is [tex]\(\frac{47}{30}\)[/tex].

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