Answer :
Certainly! Let's go through the problem step by step.
We need to calculate the product of the decimal number [tex]\(2.35\)[/tex] and the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the Fraction to a Decimal (optional):
- [tex]\(\frac{2}{3}\)[/tex] as a decimal is approximately [tex]\(0.6667\)[/tex]. While this can help us understand, we will use the fraction form for precise calculations.
2. Multiply the Decimal by the Fraction:
- Multiply [tex]\(2.35\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This can be done directly or using a calculator: [tex]\(2.35 \times \frac{2}{3} = 1.5667\)[/tex]. This is a repeating decimal, so we'll want to express it as a fraction for the options given.
3. Convert the Result to a Fraction:
- The product [tex]\(1.5667\)[/tex] can be represented more precisely as a fraction. In this case, it simplifies to [tex]\(\frac{47}{30}\)[/tex].
4. Compare to Given Options:
- From the options provided:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- We can see that none match directly the simplified fraction [tex]\(\frac{47}{30}\)[/tex].
Based on the result we calculated, [tex]\(\frac{47}{30}\)[/tex] should be the simplified fraction representation of the multiplication. It appears to be an error in the options provided since none of them match this calculation. It's a good learning point to always check work or consult additional resources if something seems off with provided multiple-choice answers.
We need to calculate the product of the decimal number [tex]\(2.35\)[/tex] and the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the Fraction to a Decimal (optional):
- [tex]\(\frac{2}{3}\)[/tex] as a decimal is approximately [tex]\(0.6667\)[/tex]. While this can help us understand, we will use the fraction form for precise calculations.
2. Multiply the Decimal by the Fraction:
- Multiply [tex]\(2.35\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- This can be done directly or using a calculator: [tex]\(2.35 \times \frac{2}{3} = 1.5667\)[/tex]. This is a repeating decimal, so we'll want to express it as a fraction for the options given.
3. Convert the Result to a Fraction:
- The product [tex]\(1.5667\)[/tex] can be represented more precisely as a fraction. In this case, it simplifies to [tex]\(\frac{47}{30}\)[/tex].
4. Compare to Given Options:
- From the options provided:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- We can see that none match directly the simplified fraction [tex]\(\frac{47}{30}\)[/tex].
Based on the result we calculated, [tex]\(\frac{47}{30}\)[/tex] should be the simplified fraction representation of the multiplication. It appears to be an error in the options provided since none of them match this calculation. It's a good learning point to always check work or consult additional resources if something seems off with provided multiple-choice answers.
