Answer :
To solve the problem [tex]\(2.35 \cdot \frac{2}{3}\)[/tex], we need to follow these steps:
1. Convert the Decimal to a Fraction:
- First, let's represent [tex]\(2.35\)[/tex] as a fraction.
- [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex] because moving the decimal two places to the right gives us 235, and since we moved the decimal two places, we divide by 100.
2. Multiply the Fractions:
- Now we need to multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- To multiply two fractions, you simply multiply the numerators together and the denominators together:
[tex]\[
\frac{235 \cdot 2}{100 \cdot 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- To simplify [tex]\(\frac{470}{300}\)[/tex], we find the greatest common divisor (GCD) of 470 and 300.
- The GCD of 470 and 300 is 10.
- Divide both the numerator and the denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the answer is [tex]\(\frac{47}{30}\)[/tex].
Thus, [tex]\(2.35 \cdot \frac{2}{3} = \frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
- First, let's represent [tex]\(2.35\)[/tex] as a fraction.
- [tex]\(2.35\)[/tex] can be written as [tex]\(\frac{235}{100}\)[/tex] because moving the decimal two places to the right gives us 235, and since we moved the decimal two places, we divide by 100.
2. Multiply the Fractions:
- Now we need to multiply [tex]\(\frac{235}{100}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- To multiply two fractions, you simply multiply the numerators together and the denominators together:
[tex]\[
\frac{235 \cdot 2}{100 \cdot 3} = \frac{470}{300}
\][/tex]
3. Simplify the Fraction:
- To simplify [tex]\(\frac{470}{300}\)[/tex], we find the greatest common divisor (GCD) of 470 and 300.
- The GCD of 470 and 300 is 10.
- Divide both the numerator and the denominator by 10:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the answer is [tex]\(\frac{47}{30}\)[/tex].
Thus, [tex]\(2.35 \cdot \frac{2}{3} = \frac{47}{30}\)[/tex].
