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Answer :
To solve the multiplication [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we can break it down into simple steps:
1. Convert the Decimal to a Fraction: The number 2.35 can be expressed as [tex]\(\frac{235}{100}\)[/tex]. This step is optional but helps understand how fractions and decimals relate to each other.
2. Multiply the Fractions: Multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction: Now, simplify [tex]\(\frac{470}{300}\)[/tex]. We can divide both the numerator and the denominator by the greatest common divisor (GCD). In this case, the GCD of 470 and 300 is 10:
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So the final answer is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction: The number 2.35 can be expressed as [tex]\(\frac{235}{100}\)[/tex]. This step is optional but helps understand how fractions and decimals relate to each other.
2. Multiply the Fractions: Multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{235}{100} \times \frac{2}{3} = \frac{235 \times 2}{100 \times 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction: Now, simplify [tex]\(\frac{470}{300}\)[/tex]. We can divide both the numerator and the denominator by the greatest common divisor (GCD). In this case, the GCD of 470 and 300 is 10:
[tex]\[
\frac{470}{300} = \frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So the final answer is [tex]\(\frac{47}{30}\)[/tex].
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