College

Calculate the product:

[tex]\[ 2.35 \cdot \frac{2}{3} = \][/tex]

Choose the correct answer:

A. [tex]\(\frac{7}{30}\)[/tex]

B. [tex]\(\frac{7}{15}\)[/tex]

C. [tex]\(\frac{27}{30}\)[/tex]

D. [tex]\(\frac{47}{30}\)[/tex]

Answer :

To solve the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we can break it down into simple steps:

1. Convert the Decimal to a Fraction: The number 2.35 can be expressed as [tex]\(\frac{235}{100}\)[/tex]. This step is optional but helps understand how fractions and decimals relate to each other.

2. Multiply the Fractions: Multiply [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 Fraction: Now, simplify [tex]\(\frac{470}{300}\)[/tex]. We can divide both the numerator and the denominator by the greatest common divisor (GCD). In this case, the GCD of 470 and 300 is 10:
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]

So the final answer is [tex]\(\frac{47}{30}\)[/tex].