Answer :
To solve the problem of multiplying [tex]\(2.35\)[/tex] by [tex]\(\frac{2}{3}\)[/tex], let's break it down into simple steps.
1. Convert the Decimal to a Fraction:
- First, we'll need to convert the decimal number [tex]\(2.35\)[/tex] into a fraction. To do this, we note that [tex]\(2.35\)[/tex] is the same as [tex]\(\frac{235}{100}\)[/tex] because there are two decimal places.
- Simply the fraction [tex]\(\frac{235}{100}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 5. So, [tex]\(\frac{235}{100}\)[/tex] simplifies to [tex]\(\frac{47}{20}\)[/tex].
2. Multiply the Fractions:
- Now, multiply the simplified fraction [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- To multiply these fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{47}{20} \cdot \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Result:
- Next, simplify the fraction [tex]\(\frac{94}{60}\)[/tex].
- Find the greatest common divisor of 94 and 60, which is 2.
- Divide the numerator and the denominator by 2:
[tex]\[
\frac{94}{60} = \frac{47}{30}
\][/tex]
So, the result of [tex]\(2.35 \times \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
1. Convert the Decimal to a Fraction:
- First, we'll need to convert the decimal number [tex]\(2.35\)[/tex] into a fraction. To do this, we note that [tex]\(2.35\)[/tex] is the same as [tex]\(\frac{235}{100}\)[/tex] because there are two decimal places.
- Simply the fraction [tex]\(\frac{235}{100}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor, which is 5. So, [tex]\(\frac{235}{100}\)[/tex] simplifies to [tex]\(\frac{47}{20}\)[/tex].
2. Multiply the Fractions:
- Now, multiply the simplified fraction [tex]\(\frac{47}{20}\)[/tex] by [tex]\(\frac{2}{3}\)[/tex].
- To multiply these fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{47}{20} \cdot \frac{2}{3} = \frac{47 \times 2}{20 \times 3} = \frac{94}{60}
\][/tex]
3. Simplify the Result:
- Next, simplify the fraction [tex]\(\frac{94}{60}\)[/tex].
- Find the greatest common divisor of 94 and 60, which is 2.
- Divide the numerator and the denominator by 2:
[tex]\[
\frac{94}{60} = \frac{47}{30}
\][/tex]
So, the result of [tex]\(2.35 \times \frac{2}{3}\)[/tex] is [tex]\(\frac{47}{30}\)[/tex].
