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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 :

Certainly! Let's find the result of the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex].

1. Understanding the Problem:
- We need to multiply the decimal number 2.35 by the fraction [tex]\(\frac{2}{3}\)[/tex].

2. Convert Decimal to Fraction (if necessary):
- 2.35 can also be written as a fraction. However, since we are directly multiplying it with [tex]\(\frac{2}{3}\)[/tex], we'll focus on the multiplication first.

3. Perform the Multiplication:
- Multiply the decimal 2.35 by [tex]\(\frac{2}{3}\)[/tex].

4. Calculate the Result:
- [tex]\(2.35 \times \frac{2}{3} = 1.566666...\)[/tex] (a repeating decimal).

5. Express the Result as a Fraction:
- Convert the decimal result [tex]\(1.566666...\)[/tex] into a fraction. The repeating decimal converts to [tex]\(\frac{47}{30}\)[/tex].

6. Choose the Correct Answer:
- Among the given options:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]

- The fraction that matches our result is [tex]\(\frac{47}{30}\)[/tex].

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

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