Calculate the following expression:

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

Choose the correct answer:

A. \(\frac{7}{30}\)

B. \(\frac{7}{15}\)

C. \(\frac{27}{30}\)

D. \(\frac{47}{30}\)

Question

High School

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Answer :

danjohnbrain danjohnbrain · Answer 1 · 2024-12-20T07:45:38-05:00

To solve the expression [tex]2.35 \cdot \frac{2}{3}[/tex], we need to multiply the decimal 2.35 by the fraction [tex]\frac{2}{3}[/tex].

Step 1: Convert the decimal to a fraction.

2.35 as a fraction is [tex]\frac{235}{100}[/tex], since there are two decimal places.

Step 2: Multiply the fractions.

Now, we multiply the fractions [tex]\frac{235}{100} \cdot \frac{2}{3}[/tex].

[tex]\frac{235 \times 2}{100 \times 3} = \frac{470}{300}[/tex]

Step 3: Simplify the fraction.

To simplify [tex]\frac{470}{300}[/tex], we find 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 expression [tex]2.35 \cdot \frac{2}{3} = \frac{47}{30}[/tex].

So, the correct answer is option D: [tex]\frac{47}{30}[/tex].