Answer :
Certainly! Let's break down the problem step-by-step.
We need to find the result of multiplying [tex]\( 2.35 \)[/tex] by [tex]\( \frac{2}{3} \)[/tex].
1. Convert the multiplication:
First, we multiply [tex]\( 2.35 \)[/tex] by [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
2.35 \cdot \frac{2}{3}
\][/tex]
2. Multiply the numerator:
Multiply [tex]\( 2.35 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[
2.35 \times 2 = 4.70
\][/tex]
3. Keep the denominator the same:
The denominator remains [tex]\( 3 \)[/tex]. Therefore, we now have:
[tex]\[
\frac{4.70}{3}
\][/tex]
4. Perform the division:
Divide the numerator [tex]\( 4.70 \)[/tex] by the denominator [tex]\( 3 \)[/tex]:
[tex]\[
\frac{4.70}{3} = 1.5666666666666667
\][/tex]
5. Express as a fraction:
Since the answer must be expressed as a fraction, the result [tex]\( 4.70 \div 3 \)[/tex] should be considered for fractional form:
According to earlier simplifications:
[tex]\[
\frac{4.70}{3} = \frac{5291729562160333}{3377699720527872}
\][/tex]
6. Analyze the given options:
Compare this value with the provided options:
[tex]\[
\frac{7}{30}, \quad \frac{7}{15}, \quad \frac{27}{30}, \quad \frac{47}{30}
\][/tex]
By a closer look, none of these fractions exactly match [tex]\(\frac{5291729562160333}{3377699720527872}\)[/tex].
However, let's see if any provided options represent 1.5666666666666667 (the decimal form obtained):
- [tex]\(\frac{7}{30} \approx 0.2333\)[/tex]
- [tex]\(\frac{7}{15} \approx 0.4667\)[/tex]
- [tex]\(\frac{27}{30} \approx 0.9\)[/tex]
- [tex]\(\frac{47}{30} \approx 1.5666666666666667\)[/tex]
Clearly, [tex]\(\frac{47}{30} = 1.5666666666666667\)[/tex] is the correct match.
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
We need to find the result of multiplying [tex]\( 2.35 \)[/tex] by [tex]\( \frac{2}{3} \)[/tex].
1. Convert the multiplication:
First, we multiply [tex]\( 2.35 \)[/tex] by [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
2.35 \cdot \frac{2}{3}
\][/tex]
2. Multiply the numerator:
Multiply [tex]\( 2.35 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[
2.35 \times 2 = 4.70
\][/tex]
3. Keep the denominator the same:
The denominator remains [tex]\( 3 \)[/tex]. Therefore, we now have:
[tex]\[
\frac{4.70}{3}
\][/tex]
4. Perform the division:
Divide the numerator [tex]\( 4.70 \)[/tex] by the denominator [tex]\( 3 \)[/tex]:
[tex]\[
\frac{4.70}{3} = 1.5666666666666667
\][/tex]
5. Express as a fraction:
Since the answer must be expressed as a fraction, the result [tex]\( 4.70 \div 3 \)[/tex] should be considered for fractional form:
According to earlier simplifications:
[tex]\[
\frac{4.70}{3} = \frac{5291729562160333}{3377699720527872}
\][/tex]
6. Analyze the given options:
Compare this value with the provided options:
[tex]\[
\frac{7}{30}, \quad \frac{7}{15}, \quad \frac{27}{30}, \quad \frac{47}{30}
\][/tex]
By a closer look, none of these fractions exactly match [tex]\(\frac{5291729562160333}{3377699720527872}\)[/tex].
However, let's see if any provided options represent 1.5666666666666667 (the decimal form obtained):
- [tex]\(\frac{7}{30} \approx 0.2333\)[/tex]
- [tex]\(\frac{7}{15} \approx 0.4667\)[/tex]
- [tex]\(\frac{27}{30} \approx 0.9\)[/tex]
- [tex]\(\frac{47}{30} \approx 1.5666666666666667\)[/tex]
Clearly, [tex]\(\frac{47}{30} = 1.5666666666666667\)[/tex] is the correct match.
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{47}{30}}
\][/tex]
