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:
- First, we need to convert the decimal 2.35 to a fraction. The decimal 2.35 is equivalent to the fraction [tex]\(\frac{235}{100}\)[/tex]. This is because moving the decimal two places to the right makes it 235, and we divide by 100 to adjust for those two places.
2. Simplify the Fraction:
- The fraction [tex]\(\frac{235}{100}\)[/tex] can be simplified. The greatest common divisor of 235 and 100 is 5. Divide both the numerator and the denominator by 5:
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
3. Multiply the Fractions:
- Now that we have [tex]\(\frac{47}{20}\)[/tex], we multiply this by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{47}{20} \times \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
4. Simplify the Resulting Fraction:
- Simplify [tex]\(\frac{94}{60}\)[/tex]. The greatest common divisor of 94 and 60 is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
So, the final answer is [tex]\(\frac{47}{30}\)[/tex], which corresponds to the fourth option in the list given: [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
- First, we need to convert the decimal 2.35 to a fraction. The decimal 2.35 is equivalent to the fraction [tex]\(\frac{235}{100}\)[/tex]. This is because moving the decimal two places to the right makes it 235, and we divide by 100 to adjust for those two places.
2. Simplify the Fraction:
- The fraction [tex]\(\frac{235}{100}\)[/tex] can be simplified. The greatest common divisor of 235 and 100 is 5. Divide both the numerator and the denominator by 5:
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
3. Multiply the Fractions:
- Now that we have [tex]\(\frac{47}{20}\)[/tex], we multiply this by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{47}{20} \times \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
4. Simplify the Resulting Fraction:
- Simplify [tex]\(\frac{94}{60}\)[/tex]. The greatest common divisor of 94 and 60 is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
So, the final answer is [tex]\(\frac{47}{30}\)[/tex], which corresponds to the fourth option in the list given: [tex]\(\frac{47}{30}\)[/tex].
