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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 of multiplying 2.35 by [tex]\(\frac{2}{3}\)[/tex], follow these steps:

1. Understand what the multiplication involves:
- We need to multiply 2.35, a decimal number, by [tex]\(\frac{2}{3}\)[/tex], a fraction.

2. Convert the decimal to a fraction (optional):
- Although it's not necessary, you can convert 2.35 to a fraction if you feel more comfortable working with fractions. [tex]\(2.35 = \frac{235}{100}\)[/tex].

3. Multiply the decimal by the fraction directly:
- Calculate [tex]\(2.35 \times \frac{2}{3}\)[/tex]. This is the main operation.

4. Calculate the result:
- When you multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex], you get approximately 1.56667.

5. Check which option matches this result:
- Compare the result (1.56667) with the given options:
- [tex]\(\frac{7}{30} \approx 0.2333\)[/tex]
- [tex]\(\frac{7}{15} \approx 0.4667\)[/tex]
- [tex]\(\frac{27}{30} \approx 0.9\)[/tex]
- [tex]\(\frac{47}{30} \approx 1.56667\)[/tex]

- The closest match to 1.56667 is [tex]\(\frac{47}{30}\)[/tex].

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

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