Answer :
To solve the problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we can approach it step-by-step:
1. Convert 2.35 to a Fraction:
- First, recognize that 2.35 is a decimal. We can express it as a fraction for easier computation.
- The decimal 2.35 can be written as the fraction [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions:
- Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This involves multiplying the numerators together and the denominators together:
[tex]\[
\frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300.
- The GCD of 470 and 300 is 10.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the result of multiplying [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex]. Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Convert 2.35 to a Fraction:
- First, recognize that 2.35 is a decimal. We can express it as a fraction for easier computation.
- The decimal 2.35 can be written as the fraction [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions:
- Next, multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This involves multiplying the numerators together and the denominators together:
[tex]\[
\frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- Simplify [tex]\(\frac{470}{300}\)[/tex] by finding the greatest common divisor (GCD) of 470 and 300.
- The GCD of 470 and 300 is 10.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the result of multiplying [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex]. Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
