Answer :
To solve the problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we can follow these steps:
1. Convert the Decimal to a Fraction:
First, convert the decimal number [tex]\(2.35\)[/tex] to a fraction. The decimal [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex] because [tex]\(235\)[/tex] is the numerator (the number after removing the decimal point) and the denominator is [tex]\(100\)[/tex] since [tex]\(2.35\)[/tex] has two decimal places.
2. Multiply the Fractions:
Now, we multiply the fractions [tex]\(\frac{235}{100}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex].
[tex]\[
\frac{235}{100} \cdot \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Resulting Fraction:
To simplify [tex]\(\frac{470}{300}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD is [tex]\(10\)[/tex].
Divide both the numerator and the denominator by [tex]\(10\)[/tex]:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Between the given options, [tex]\(\frac{47}{30}\)[/tex] matches one of the choices given, which confirms it as the correct answer. Therefore, [tex]\(2.35 \cdot \frac{2}{3} = \frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
First, convert the decimal number [tex]\(2.35\)[/tex] to a fraction. The decimal [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex] because [tex]\(235\)[/tex] is the numerator (the number after removing the decimal point) and the denominator is [tex]\(100\)[/tex] since [tex]\(2.35\)[/tex] has two decimal places.
2. Multiply the Fractions:
Now, we multiply the fractions [tex]\(\frac{235}{100}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex].
[tex]\[
\frac{235}{100} \cdot \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Resulting Fraction:
To simplify [tex]\(\frac{470}{300}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD is [tex]\(10\)[/tex].
Divide both the numerator and the denominator by [tex]\(10\)[/tex]:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Between the given options, [tex]\(\frac{47}{30}\)[/tex] matches one of the choices given, which confirms it as the correct answer. Therefore, [tex]\(2.35 \cdot \frac{2}{3} = \frac{47}{30}\)[/tex].
