Answer :
Sure, let's solve the problem step by step.
We are asked to find the result of multiplying the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
Step 1: Multiply the numbers
First, we multiply the decimal number [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[ 2.35 \times \frac{2}{3} = 1.566666\ldots \][/tex]
This is a repeating decimal, continuing as [tex]\(1.5666\)[/tex] with the 6 repeating.
Step 2: Convert the result to a fraction
To express the repeating decimal [tex]\(1.5666\ldots\)[/tex] as a fraction, we recognize that it can be written as a fraction. In its simplest form, the fraction that represents this repeating decimal is [tex]\(\frac{47}{30}\)[/tex].
Step 3: Compare with given options
Now, we need to find which of the given options matches our fraction [tex]\(\frac{47}{30}\)[/tex]:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
Clearly, the option that matches is [tex]\(\frac{47}{30}\)[/tex].
Therefore, the solution to the problem [tex]\(2.35 \times \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
So, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
We are asked to find the result of multiplying the decimal [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex].
Step 1: Multiply the numbers
First, we multiply the decimal number [tex]\(2.35\)[/tex] by the fraction [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[ 2.35 \times \frac{2}{3} = 1.566666\ldots \][/tex]
This is a repeating decimal, continuing as [tex]\(1.5666\)[/tex] with the 6 repeating.
Step 2: Convert the result to a fraction
To express the repeating decimal [tex]\(1.5666\ldots\)[/tex] as a fraction, we recognize that it can be written as a fraction. In its simplest form, the fraction that represents this repeating decimal is [tex]\(\frac{47}{30}\)[/tex].
Step 3: Compare with given options
Now, we need to find which of the given options matches our fraction [tex]\(\frac{47}{30}\)[/tex]:
- [tex]\(\frac{7}{30}\)[/tex]
- [tex]\(\frac{7}{15}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
- [tex]\(\frac{47}{30}\)[/tex]
Clearly, the option that matches is [tex]\(\frac{47}{30}\)[/tex].
Therefore, the solution to the problem [tex]\(2.35 \times \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
So, the correct answer is [tex]\(\frac{47}{30}\)[/tex].
