Answer :
To solve the question [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], let's break it down step by step.
1. Convert 2.35 to a Fraction:
- We can express 2.35 as a fraction. Since there are two decimal places in 2.35, it is equivalent to [tex]\(\frac{235}{100}\)[/tex].
- Simplify [tex]\(\frac{235}{100}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
2. Multiply by [tex]\(\frac{2}{3}\)[/tex]:
- Now, multiply the fraction [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{47}{20} \times \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Result:
- The fraction [tex]\(\frac{94}{60}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Thus, the solution to the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
1. Convert 2.35 to a Fraction:
- We can express 2.35 as a fraction. Since there are two decimal places in 2.35, it is equivalent to [tex]\(\frac{235}{100}\)[/tex].
- Simplify [tex]\(\frac{235}{100}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 5:
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
2. Multiply by [tex]\(\frac{2}{3}\)[/tex]:
- Now, multiply the fraction [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{47}{20} \times \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Result:
- The fraction [tex]\(\frac{94}{60}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
Thus, the solution to the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
