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Answer :
To solve [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we'll break it down into steps:
1. Express 2.35 as a fraction:
The number 2.35 can be written as a fraction. It is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Simplify [tex]\(\frac{235}{100}\)[/tex]:
To simplify, find the greatest common divisor of 235 and 100, which is 5.
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
3. Multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
Multiply the numerators together and the denominators together.
[tex]\[
\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}
\][/tex]
4. Simplify [tex]\(\frac{94}{60}\)[/tex]:
Find the greatest common divisor of 94 and 60, which is 2.
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
So, the product of [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] in its simplest form is [tex]\(\frac{47}{30}\)[/tex].
1. Express 2.35 as a fraction:
The number 2.35 can be written as a fraction. It is equivalent to [tex]\(\frac{235}{100}\)[/tex].
2. Simplify [tex]\(\frac{235}{100}\)[/tex]:
To simplify, find the greatest common divisor of 235 and 100, which is 5.
[tex]\[
\frac{235 \div 5}{100 \div 5} = \frac{47}{20}
\][/tex]
3. Multiply [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
Multiply the numerators together and the denominators together.
[tex]\[
\frac{47 \cdot 2}{20 \cdot 3} = \frac{94}{60}
\][/tex]
4. Simplify [tex]\(\frac{94}{60}\)[/tex]:
Find the greatest common divisor of 94 and 60, which is 2.
[tex]\[
\frac{94 \div 2}{60 \div 2} = \frac{47}{30}
\][/tex]
So, the product of [tex]\(2.35 \cdot \frac{2}{3}\)[/tex] in its simplest form is [tex]\(\frac{47}{30}\)[/tex].
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