Answer :
Sure! To solve the multiplication problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], let’s go through the steps:
1. Convert the Decimal to a Fraction:
- Start by representing [tex]\(2.35\)[/tex] as a fraction. Since [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex], let's use that form for calculation.
2. Multiply the Fractions:
- Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This is done by multiplying the numerators together and the denominators together:
[tex]\[
\frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Now, simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300, which is 10.
- Divide both the numerator and the denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Therefore, the simplified answer to the multiplication problem is [tex]\(\frac{47}{30}\)[/tex].
The correct answer from the given options is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
- Start by representing [tex]\(2.35\)[/tex] as a fraction. Since [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex], let's use that form for calculation.
2. Multiply the Fractions:
- Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This is done by multiplying the numerators together and the denominators together:
[tex]\[
\frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Now, simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300, which is 10.
- Divide both the numerator and the denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
Therefore, the simplified answer to the multiplication problem is [tex]\(\frac{47}{30}\)[/tex].
The correct answer from the given options is [tex]\(\frac{47}{30}\)[/tex].
