Answer :
To solve the question [tex]\(2.35 \cdot \frac{2}{3} \)[/tex], we need to follow these steps:
1. Multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex]:
First, convert 2.35 into a fraction or a decimal. As a decimal, it's already given. Now, multiply:
[tex]\[
2.35 \times \frac{2}{3} = \frac{2.35 \times 2}{3}
\][/tex]
Calculate the multiplication in the numerator:
[tex]\[
2.35 \times 2 = 4.7
\][/tex]
So, the expression becomes:
[tex]\[
\frac{4.7}{3}
\][/tex]
2. Convert the result to a fraction:
Next, convert the decimal 4.7 into a fraction:
[tex]\[
4.7 = \frac{47}{10}
\][/tex]
Now, divide by 3:
[tex]\[
\frac{47}{10} \times \frac{1}{3} = \frac{47}{30}
\][/tex]
3. Match the result with the given options:
Compare this calculated fraction [tex]\(\frac{47}{30}\)[/tex] with the given choices:
- [tex]\(\frac{k}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
The fraction [tex]\(\frac{47}{30}\)[/tex] matches the last option.
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex]:
First, convert 2.35 into a fraction or a decimal. As a decimal, it's already given. Now, multiply:
[tex]\[
2.35 \times \frac{2}{3} = \frac{2.35 \times 2}{3}
\][/tex]
Calculate the multiplication in the numerator:
[tex]\[
2.35 \times 2 = 4.7
\][/tex]
So, the expression becomes:
[tex]\[
\frac{4.7}{3}
\][/tex]
2. Convert the result to a fraction:
Next, convert the decimal 4.7 into a fraction:
[tex]\[
4.7 = \frac{47}{10}
\][/tex]
Now, divide by 3:
[tex]\[
\frac{47}{10} \times \frac{1}{3} = \frac{47}{30}
\][/tex]
3. Match the result with the given options:
Compare this calculated fraction [tex]\(\frac{47}{30}\)[/tex] with the given choices:
- [tex]\(\frac{k}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
The fraction [tex]\(\frac{47}{30}\)[/tex] matches the last option.
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
