College

Calculate the following:

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

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 [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], let's go through the steps to determine the correct answer.

1. Convert the Decimal to a Fraction:
- [tex]\(2.35\)[/tex] can be written as a fraction. It is equivalent to [tex]\(\frac{235}{100}\)[/tex]. This fraction simplifies to [tex]\(\frac{47}{20}\)[/tex], which is done by dividing the numerator and the denominator by their greatest common divisor, which is 5.

2. Multiply the Fractions:
- We want to multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- Multiply the numerators: [tex]\(47 \times 2 = 94\)[/tex].
- Multiply the denominators: [tex]\(20 \times 3 = 60\)[/tex].
- So, the product is [tex]\(\frac{94}{60}\)[/tex].

3. Simplify the Fraction:
- [tex]\(\frac{94}{60}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of 94 and 60. The GCD is 2.
- Divide both the numerator and denominator by 2: [tex]\(\frac{94 \div 2}{60 \div 2} = \frac{47}{30}\)[/tex].

4. Final Answer:
- The simplified form of the product is [tex]\(\frac{47}{30}\)[/tex].

Thus, the correct answer is [tex]\(\frac{47}{30}\)[/tex].