Answer :
Sure! Let's solve the math problem step by step.
We need to multiply the decimal number 2.35 by the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the decimal to a fraction:
The decimal 2.35 can be written as a fraction. Since 2.35 has two decimal places, we can write it as [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the fractions:
Next, 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 resulting fraction:
Now, simplify the fraction [tex]\(\frac{470}{300}\)[/tex]. 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 their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the simplification gives us [tex]\(\frac{47}{30}\)[/tex].
Therefore, the final answer is [tex]\(\frac{47}{30}\)[/tex].
We need to multiply the decimal number 2.35 by the fraction [tex]\(\frac{2}{3}\)[/tex].
1. Convert the decimal to a fraction:
The decimal 2.35 can be written as a fraction. Since 2.35 has two decimal places, we can write it as [tex]\(\frac{235}{100}\)[/tex].
2. Multiply the fractions:
Next, 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 resulting fraction:
Now, simplify the fraction [tex]\(\frac{470}{300}\)[/tex]. 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 their GCD:
[tex]\[
\frac{470 \div 10}{300 \div 10} = \frac{47}{30}
\][/tex]
So, the simplification gives us [tex]\(\frac{47}{30}\)[/tex].
Therefore, the final answer is [tex]\(\frac{47}{30}\)[/tex].
