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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].
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].
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