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Answer :
To solve the expression [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we will follow these steps:
1. Convert the decimal to a fraction: The number [tex]\(2.35\)[/tex] can be written as a fraction. Recall that [tex]\(2.35\)[/tex] means [tex]\(2 + 0.35\)[/tex].
- [tex]\(2.35\)[/tex] can be broken into [tex]\(2 + 0.35\)[/tex].
- The fraction equivalent of [tex]\(0.35\)[/tex] can be written as [tex]\( \frac{35}{100} \)[/tex].
2. Simplify the fraction [tex]\( \frac{35}{100} \)[/tex]:
[tex]\[
\frac{35}{100} = \frac{7}{20} \quad (\text{dividing both numerator and denominator by 5})
\][/tex]
3. Combine the fractional part with the whole number part:
[tex]\[
2.35 = 2 + \frac{7}{20} = \frac{40}{20} + \frac{7}{20} = \frac{47}{20}
\][/tex]
4. Multiply the given fractions:
[tex]\[
2.35 \cdot \frac{2}{3} = \frac{47}{20} \cdot \frac{2}{3}
\][/tex]
5. Multiply the numerators and the denominators:
[tex]\[
\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}
\][/tex]
6. Simplify the fraction [tex]\(\frac{94}{60}\)[/tex]:
- Find the greatest common divisor (GCD) of 94 and 60, which is 2.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{94}{60} = \frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Therefore, the simplified result of [tex]\( 2.35 \cdot \frac{2}{3} \)[/tex] is [tex]\( \frac{47}{30} \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
1. Convert the decimal to a fraction: The number [tex]\(2.35\)[/tex] can be written as a fraction. Recall that [tex]\(2.35\)[/tex] means [tex]\(2 + 0.35\)[/tex].
- [tex]\(2.35\)[/tex] can be broken into [tex]\(2 + 0.35\)[/tex].
- The fraction equivalent of [tex]\(0.35\)[/tex] can be written as [tex]\( \frac{35}{100} \)[/tex].
2. Simplify the fraction [tex]\( \frac{35}{100} \)[/tex]:
[tex]\[
\frac{35}{100} = \frac{7}{20} \quad (\text{dividing both numerator and denominator by 5})
\][/tex]
3. Combine the fractional part with the whole number part:
[tex]\[
2.35 = 2 + \frac{7}{20} = \frac{40}{20} + \frac{7}{20} = \frac{47}{20}
\][/tex]
4. Multiply the given fractions:
[tex]\[
2.35 \cdot \frac{2}{3} = \frac{47}{20} \cdot \frac{2}{3}
\][/tex]
5. Multiply the numerators and the denominators:
[tex]\[
\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}
\][/tex]
6. Simplify the fraction [tex]\(\frac{94}{60}\)[/tex]:
- Find the greatest common divisor (GCD) of 94 and 60, which is 2.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{94}{60} = \frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Therefore, the simplified result of [tex]\( 2.35 \cdot \frac{2}{3} \)[/tex] is [tex]\( \frac{47}{30} \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
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