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Answer :
To solve the problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], let's break it down step by step:
1. Convert the Decimal to a Fraction:
The decimal 2.35 can be rewritten as a fraction. It is equal to [tex]\(\frac{235}{100}\)[/tex], since 2.35 means 2 wholes and 35 hundredths. We can simplify this fraction to [tex]\(\frac{47}{20}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
2. Multiply the Fractions:
Now, we need to multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]. To do this, multiply the numerators together and the denominators together:
[tex]\[
\frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Resulting Fraction:
The fraction [tex]\(\frac{94}{60}\)[/tex] can be simplified by finding the greatest common divisor of 94 and 60, which is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Now, we have the final answer:
[tex]\[
2.35 \cdot \frac{2}{3} = \frac{47}{30}
\][/tex]
Therefore, the correct option from the given choices is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
The decimal 2.35 can be rewritten as a fraction. It is equal to [tex]\(\frac{235}{100}\)[/tex], since 2.35 means 2 wholes and 35 hundredths. We can simplify this fraction to [tex]\(\frac{47}{20}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
2. Multiply the Fractions:
Now, we need to multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]. To do this, multiply the numerators together and the denominators together:
[tex]\[
\frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Resulting Fraction:
The fraction [tex]\(\frac{94}{60}\)[/tex] can be simplified by finding the greatest common divisor of 94 and 60, which is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Now, we have the final answer:
[tex]\[
2.35 \cdot \frac{2}{3} = \frac{47}{30}
\][/tex]
Therefore, the correct option from the given choices is [tex]\(\frac{47}{30}\)[/tex].
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