Answer :
To find the value of [tex]\( 2.35 \cdot \frac{2}{3} \)[/tex], follow these steps:
1. Convert the decimal to a fraction if needed:
- You don't need to convert here as we will use the decimal directly.
2. Multiply the decimal by the fraction:
- [tex]\( 2.35 \times \frac{2}{3} \)[/tex]
3. Perform the multiplication:
- First, multiply the decimal by the numerator of the fraction:
[tex]\( 2.35 \times 2 = 4.70 \)[/tex]
- Next, divide the resulting product by the denominator of the fraction:
[tex]\( \frac{4.70}{3} = 1.5666666666666667 \)[/tex] (approximately 1.57, but we will use more precise value.)
Now, let's compare this result with the given answer choices which are in fraction form:
- [tex]\( \frac{7}{30} \approx 0.2333 \)[/tex]
- [tex]\( \frac{7}{15} \approx 0.4667 \)[/tex]
- [tex]\( \frac{27}{30} = 0.9 \)[/tex]
- [tex]\( \frac{47}{30} \approx 1.5666666666666667 \)[/tex]
From these comparisons, we see that:
[tex]\( \frac{47}{30} \approx 1.5666666666666667 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{47}{30}} \][/tex]
1. Convert the decimal to a fraction if needed:
- You don't need to convert here as we will use the decimal directly.
2. Multiply the decimal by the fraction:
- [tex]\( 2.35 \times \frac{2}{3} \)[/tex]
3. Perform the multiplication:
- First, multiply the decimal by the numerator of the fraction:
[tex]\( 2.35 \times 2 = 4.70 \)[/tex]
- Next, divide the resulting product by the denominator of the fraction:
[tex]\( \frac{4.70}{3} = 1.5666666666666667 \)[/tex] (approximately 1.57, but we will use more precise value.)
Now, let's compare this result with the given answer choices which are in fraction form:
- [tex]\( \frac{7}{30} \approx 0.2333 \)[/tex]
- [tex]\( \frac{7}{15} \approx 0.4667 \)[/tex]
- [tex]\( \frac{27}{30} = 0.9 \)[/tex]
- [tex]\( \frac{47}{30} \approx 1.5666666666666667 \)[/tex]
From these comparisons, we see that:
[tex]\( \frac{47}{30} \approx 1.5666666666666667 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{47}{30}} \][/tex]
