Answer :
To solve the multiplication of a decimal and a fraction, follow these steps:
1. Understand the Problem: You need to multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Decimal to a Fraction:
- The decimal 2.35 can be expressed as [tex]\(\frac{235}{100}\)[/tex] by recognizing that 2.35 is the same as [tex]\(2\)[/tex] whole and [tex]\(35\)[/tex] hundredths.
3. Simplify the Fraction:
- [tex]\(\frac{235}{100}\)[/tex] can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
- [tex]\(\frac{235 \div 5}{100 \div 5} = \frac{47}{20}\)[/tex].
4. Multiply Two Fractions:
- Now multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
- [tex]\(\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}\)[/tex].
5. Simplify the Resulting Fraction:
- To simplify [tex]\(\frac{94}{60}\)[/tex], find the greatest common divisor of 94 and 60, which is 2.
- [tex]\(\frac{94 \div 2}{60 \div 2} = \frac{47}{30}\)[/tex].
Therefore, the product of 2.35 and [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex], which matches one of the given options. So, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
1. Understand the Problem: You need to multiply 2.35 by [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Decimal to a Fraction:
- The decimal 2.35 can be expressed as [tex]\(\frac{235}{100}\)[/tex] by recognizing that 2.35 is the same as [tex]\(2\)[/tex] whole and [tex]\(35\)[/tex] hundredths.
3. Simplify the Fraction:
- [tex]\(\frac{235}{100}\)[/tex] can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
- [tex]\(\frac{235 \div 5}{100 \div 5} = \frac{47}{20}\)[/tex].
4. Multiply Two Fractions:
- Now multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
- [tex]\(\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}\)[/tex].
5. Simplify the Resulting Fraction:
- To simplify [tex]\(\frac{94}{60}\)[/tex], find the greatest common divisor of 94 and 60, which is 2.
- [tex]\(\frac{94 \div 2}{60 \div 2} = \frac{47}{30}\)[/tex].
Therefore, the product of 2.35 and [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex], which matches one of the given options. So, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
