High School

Calculate the following expression:

\[ 2.35 \cdot \frac{2}{3} \]

A. \(\frac{7}{30}\)
B. \(\frac{7}{15}\)
C. \(\frac{27}{30}\)
D. \(\frac{47}{30}\)

Answer :

To solve the question [tex]\( 2.35 \cdot \frac{2}{3} \)[/tex], follow these steps:

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

2. Convert the decimal to a fraction or keep it as it is: In this case, we can multiply directly using the decimal.

3. Perform the multiplication:
- Multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex].
- This involves multiplying the decimal directly by the numerator of the fraction and then dividing the result by the denominator of the fraction.
- Calculation: [tex]\(2.35 \times 2 = 4.70\)[/tex].
- Now divide by 3: [tex]\(\frac{4.70}{3} \approx 1.5667\)[/tex].

4. Convert the result to a fraction (if needed or applicable):
- The approximate decimal result 1.5667 can be expressed as a more precise fraction.
- The fractional form that most accurately represents this value within standard mathematical limits is [tex]\(\frac{47}{30}\)[/tex].

5. Conclusion:
- The calculation results in a value of approximately 1.567 which is represented by [tex]\(\frac{47}{30}\)[/tex].

Thus, the correct answer among the options given is [tex]\(\frac{47}{30}\)[/tex].