Answer :
To solve the problem of multiplying [tex]\(2.35\)[/tex] by [tex]\(\frac{2}{3}\)[/tex], we can follow these steps:
1. Multiply the Decimal and the Fraction:
- Start by multiplying the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
- First, multiply [tex]\(2.35\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
2.35 \times 2 = 4.7
\][/tex]
- Then, divide this result by [tex]\(3\)[/tex]:
[tex]\[
\frac{4.7}{3} = 1.56667 \ldots
\][/tex]
2. Convert the Result to a Fraction:
- The result, [tex]\(1.56667\ldots\)[/tex], needs to be expressed as a fraction.
- Converting the repeating decimal [tex]\(1.56667\ldots\)[/tex] to a fraction, we get [tex]\(\frac{47}{30}\)[/tex].
Thus, the answer to the question [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is:
[tex]\[
\frac{47}{30}
\][/tex]
This matches one of the choices given in the question.
1. Multiply the Decimal and the Fraction:
- Start by multiplying the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
- First, multiply [tex]\(2.35\)[/tex] by [tex]\(2\)[/tex]:
[tex]\[
2.35 \times 2 = 4.7
\][/tex]
- Then, divide this result by [tex]\(3\)[/tex]:
[tex]\[
\frac{4.7}{3} = 1.56667 \ldots
\][/tex]
2. Convert the Result to a Fraction:
- The result, [tex]\(1.56667\ldots\)[/tex], needs to be expressed as a fraction.
- Converting the repeating decimal [tex]\(1.56667\ldots\)[/tex] to a fraction, we get [tex]\(\frac{47}{30}\)[/tex].
Thus, the answer to the question [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is:
[tex]\[
\frac{47}{30}
\][/tex]
This matches one of the choices given in the question.
