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Answer :
To solve the problem of multiplying [tex]\(2.35 \times \frac{2}{3}\)[/tex], follow these steps:
1. Convert the Decimal to a Fraction: Start by converting the decimal 2.35 into a fraction. The decimal 2.35 can be written as [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions: Next, 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]. To do this, find the greatest common divisor (GCD) of 470 and 300. The GCD is 10. Divide both the numerator and the denominator by 10.
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
4. Verify Which Option Matches: Compare [tex]\(\frac{47}{30}\)[/tex] to the options provided:
[tex]\[
\frac{7}{30}, \quad \frac{7}{15}, \quad \frac{27}{30}, \quad \frac{47}{30}
\][/tex]
We find that the simplified result [tex]\(\frac{47}{30}\)[/tex] matches one of the options given: [tex]\(\frac{47}{30}\)[/tex].
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction: Start by converting the decimal 2.35 into a fraction. The decimal 2.35 can be written as [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the Fractions: Next, 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]. To do this, find the greatest common divisor (GCD) of 470 and 300. The GCD is 10. Divide both the numerator and the denominator by 10.
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
4. Verify Which Option Matches: Compare [tex]\(\frac{47}{30}\)[/tex] to the options provided:
[tex]\[
\frac{7}{30}, \quad \frac{7}{15}, \quad \frac{27}{30}, \quad \frac{47}{30}
\][/tex]
We find that the simplified result [tex]\(\frac{47}{30}\)[/tex] matches one of the options given: [tex]\(\frac{47}{30}\)[/tex].
Therefore, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
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