Answer :
Sure, let's solve the given problem step by step.
First, we need to multiply the decimal number [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the decimal to a fraction (if needed):
Since we are given [tex]\(2.35\)[/tex] as a decimal, let's keep it as is for now.
2. Multiply the decimal by the fraction:
[tex]\[
2.35 \times \frac{2}{3}
\][/tex]
3. First, divide [tex]\(2\)[/tex] by [tex]\(3\)[/tex] to get the fractional part:
[tex]\[
\frac{2}{3} \approx 0.6667
\][/tex]
4. Next, multiply [tex]\(2.35\)[/tex] by [tex]\(0.6667\)[/tex]:
[tex]\[
2.35 \times 0.6667 \approx 1.5666666666666667
\][/tex]
So, the product of [tex]\(2.35\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] is approximately [tex]\(1.5666666666666667\)[/tex].
Now, let's compare this with the fractions provided in the answers:
[tex]\[
\frac{7}{30}, \frac{7}{15}, \frac{27}{30}, \frac{47}{30}
\][/tex]
We can convert these fractions to decimals:
1. [tex]\(\frac{7}{30}\)[/tex]:
[tex]\[
\frac{7}{30} \approx 0.2333
\][/tex]
2. [tex]\(\frac{7}{15}\)[/tex]:
[tex]\[
\frac{7}{15} \approx 0.4667
\][/tex]
3. [tex]\(\frac{27}{30}\)[/tex]:
[tex]\[
\frac{27}{30} = 0.9
\][/tex]
4. [tex]\(\frac{47}{30}\)[/tex]:
[tex]\[
\frac{47}{30} \approx 1.5666666666666667
\][/tex]
Comparing [tex]\(1.5666666666666667\)[/tex] with the given options, we see that it matches exactly with [tex]\(\frac{47}{30}\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
First, we need to multiply the decimal number [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the decimal to a fraction (if needed):
Since we are given [tex]\(2.35\)[/tex] as a decimal, let's keep it as is for now.
2. Multiply the decimal by the fraction:
[tex]\[
2.35 \times \frac{2}{3}
\][/tex]
3. First, divide [tex]\(2\)[/tex] by [tex]\(3\)[/tex] to get the fractional part:
[tex]\[
\frac{2}{3} \approx 0.6667
\][/tex]
4. Next, multiply [tex]\(2.35\)[/tex] by [tex]\(0.6667\)[/tex]:
[tex]\[
2.35 \times 0.6667 \approx 1.5666666666666667
\][/tex]
So, the product of [tex]\(2.35\)[/tex] and [tex]\(\frac{2}{3}\)[/tex] is approximately [tex]\(1.5666666666666667\)[/tex].
Now, let's compare this with the fractions provided in the answers:
[tex]\[
\frac{7}{30}, \frac{7}{15}, \frac{27}{30}, \frac{47}{30}
\][/tex]
We can convert these fractions to decimals:
1. [tex]\(\frac{7}{30}\)[/tex]:
[tex]\[
\frac{7}{30} \approx 0.2333
\][/tex]
2. [tex]\(\frac{7}{15}\)[/tex]:
[tex]\[
\frac{7}{15} \approx 0.4667
\][/tex]
3. [tex]\(\frac{27}{30}\)[/tex]:
[tex]\[
\frac{27}{30} = 0.9
\][/tex]
4. [tex]\(\frac{47}{30}\)[/tex]:
[tex]\[
\frac{47}{30} \approx 1.5666666666666667
\][/tex]
Comparing [tex]\(1.5666666666666667\)[/tex] with the given options, we see that it matches exactly with [tex]\(\frac{47}{30}\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
