Answer :
To solve the problem of finding the value of [tex]\(2.35 \times \frac{2}{3}\)[/tex], follow these steps:
1. Convert the Decimal to a Fraction:
- Start with the decimal 2.35. We can convert 2.35 to a fraction for more precise calculations.
- Recognize that 2.35 is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions:
- Now, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]. When multiplying fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
- The calculation would be:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Next, simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300, which is 10.
- Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
4. Select the Correct Answer:
- The simplified result is [tex]\(\frac{47}{30}\)[/tex], which matches one of the given answer choices.
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
- Start with the decimal 2.35. We can convert 2.35 to a fraction for more precise calculations.
- Recognize that 2.35 is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions:
- Now, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]. When multiplying fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
- The calculation would be:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Next, simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300, which is 10.
- Divide the numerator and the denominator by their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
4. Select the Correct Answer:
- The simplified result is [tex]\(\frac{47}{30}\)[/tex], which matches one of the given answer choices.
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
