Answer :
To find the solution to [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], let's follow a step-by-step process:
1. Understand the Expression: We need to multiply the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Decimal to a Fraction (for easier multiplication with another fraction):
- [tex]\(2.35\)[/tex] can be expressed as a fraction: [tex]\(\frac{235}{100}\)[/tex].
3. Multiply the Fractions:
- Multiply the numerators: [tex]\(235 \times 2 = 470\)[/tex].
- Multiply the denominators: [tex]\(100 \times 3 = 300\)[/tex].
- So, the product is [tex]\(\frac{470}{300}\)[/tex].
4. Simplify the Fraction:
- Divide both numerator and denominator by their greatest common divisor, which is 10.
- [tex]\(\frac{470}{300}\)[/tex] simplifies to [tex]\(\frac{47}{30}\)[/tex].
Therefore, the result of [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex], which matches one of the provided answers.
1. Understand the Expression: We need to multiply the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
2. Convert the Decimal to a Fraction (for easier multiplication with another fraction):
- [tex]\(2.35\)[/tex] can be expressed as a fraction: [tex]\(\frac{235}{100}\)[/tex].
3. Multiply the Fractions:
- Multiply the numerators: [tex]\(235 \times 2 = 470\)[/tex].
- Multiply the denominators: [tex]\(100 \times 3 = 300\)[/tex].
- So, the product is [tex]\(\frac{470}{300}\)[/tex].
4. Simplify the Fraction:
- Divide both numerator and denominator by their greatest common divisor, which is 10.
- [tex]\(\frac{470}{300}\)[/tex] simplifies to [tex]\(\frac{47}{30}\)[/tex].
Therefore, the result of [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex], which matches one of the provided answers.
