Answer :
To solve the problem of multiplying 2.35 by [tex]\(\frac{2}{3}\)[/tex], follow these steps:
1. Understand the Multiplication:
We need to multiply a decimal number (2.35) by the fraction [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Fraction:
The fraction [tex]\(\frac{2}{3}\)[/tex] needs to be converted into a decimal to perform multiplication with 2.35.
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex] (when expressed as a decimal).
3. Perform the Multiplication:
Multiply the decimal value 2.35 by 0.6667:
- [tex]\(2.35 \times 0.6667 \approx 1.5667\)[/tex].
4. Convert Result to a Fraction:
The result, 1.5667, can be converted back to a fraction:
- A close approximation is [tex]\(\frac{47}{30}\)[/tex].
5. Check with Answer Options:
Compare this fraction ([tex]\(\frac{47}{30}\)[/tex]) to the given choices:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Understand the Multiplication:
We need to multiply a decimal number (2.35) by the fraction [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Fraction:
The fraction [tex]\(\frac{2}{3}\)[/tex] needs to be converted into a decimal to perform multiplication with 2.35.
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex] (when expressed as a decimal).
3. Perform the Multiplication:
Multiply the decimal value 2.35 by 0.6667:
- [tex]\(2.35 \times 0.6667 \approx 1.5667\)[/tex].
4. Convert Result to a Fraction:
The result, 1.5667, can be converted back to a fraction:
- A close approximation is [tex]\(\frac{47}{30}\)[/tex].
5. Check with Answer Options:
Compare this fraction ([tex]\(\frac{47}{30}\)[/tex]) to the given choices:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
