Answer :
To solve the problem of multiplying a decimal by a fraction, we need to follow these steps:
1. Convert the Decimal to a Fraction:
The decimal number 2.35 can be converted to a fraction.
[tex]\(2.35\)[/tex] is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Multiply Fractions:
Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\(\frac{470}{300}\)[/tex] if possible. To do this, find the greatest common divisor (GCD) of 470 and 300, which is 10, and divide both the numerator and the denominator by this number:
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Therefore, after performing these calculations, the simplified answer is [tex]\(\frac{47}{30}\)[/tex]. This matches one of the options given in the problem, confirming it as the correct answer.
1. Convert the Decimal to a Fraction:
The decimal number 2.35 can be converted to a fraction.
[tex]\(2.35\)[/tex] is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Multiply Fractions:
Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
When multiplying fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\(\frac{470}{300}\)[/tex] if possible. To do this, find the greatest common divisor (GCD) of 470 and 300, which is 10, and divide both the numerator and the denominator by this number:
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Therefore, after performing these calculations, the simplified answer is [tex]\(\frac{47}{30}\)[/tex]. This matches one of the options given in the problem, confirming it as the correct answer.
