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Answer :
To solve the problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], follow these steps:
1. Convert the Decimal to a Fraction: Begin by expressing the decimal 2.35 as a fraction. A decimal like 2.35 can be written as [tex]\(\frac{235}{100}\)[/tex] because 2.35 is the same as 235 hundredths.
2. Multiply the Fractions: Multiply the fraction [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Resulting Fraction: Simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of the numerator and the denominator, if necessary. The GCD of 470 and 300 is 10. Divide both the numerator and denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Hence, the product [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] simplifies to [tex]\(\frac{47}{30}\)[/tex].
So, the answer to the question is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction: Begin by expressing the decimal 2.35 as a fraction. A decimal like 2.35 can be written as [tex]\(\frac{235}{100}\)[/tex] because 2.35 is the same as 235 hundredths.
2. Multiply the Fractions: Multiply the fraction [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Resulting Fraction: Simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of the numerator and the denominator, if necessary. The GCD of 470 and 300 is 10. Divide both the numerator and denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Hence, the product [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] simplifies to [tex]\(\frac{47}{30}\)[/tex].
So, the answer to the question is [tex]\(\frac{47}{30}\)[/tex].
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