Answer :
To solve the problem of multiplying the decimal 2.35 by the fraction [tex]\(\frac{2}{3}\)[/tex], we need to follow a few steps:
1. Multiply the Decimal by the Fraction:
Start by multiplying the decimal value by the fraction. When you multiply:
[tex]\[
2.35 \times \frac{2}{3} = 1.56666666667
\][/tex]
The result is approximately 1.5667.
2. Convert the Result to a Fraction:
This decimal result needs to be expressed as a fraction. When converted, it becomes:
[tex]\[
\frac{47}{30}
\][/tex]
3. Simplify and Compare:
Now, let's compare this fraction with the given options:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
The fraction [tex]\(\frac{47}{30}\)[/tex] matches exactly with one of the provided options.
Therefore, the correct answer to the problem is [tex]\(\frac{47}{30}\)[/tex].
1. Multiply the Decimal by the Fraction:
Start by multiplying the decimal value by the fraction. When you multiply:
[tex]\[
2.35 \times \frac{2}{3} = 1.56666666667
\][/tex]
The result is approximately 1.5667.
2. Convert the Result to a Fraction:
This decimal result needs to be expressed as a fraction. When converted, it becomes:
[tex]\[
\frac{47}{30}
\][/tex]
3. Simplify and Compare:
Now, let's compare this fraction with the given options:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
The fraction [tex]\(\frac{47}{30}\)[/tex] matches exactly with one of the provided options.
Therefore, the correct answer to the problem is [tex]\(\frac{47}{30}\)[/tex].
