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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].
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].
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