Sure, let's break down the problem step by step.
1. Understand the Given Percentage: We have a mixed number in the form of a percentage: [tex]\( 21 \frac{2}{3} \% \)[/tex].
2. Convert the Mixed Number to an Improper Fraction: First, we need to convert [tex]\( 21 \frac{2}{3} \)[/tex] to an improper fraction.
- The whole number part is 21.
- The fractional part is [tex]\( \frac{2}{3} \)[/tex].
- To combine these, we multiply the whole number by the denominator of the fractional part and add the numerator:
[tex]\[
21 \frac{2}{3} = 21 + \frac{2}{3} = \frac{21 \times 3 + 2}{3} = \frac{63 + 2}{3} = \frac{65}{3}
\][/tex]
3. Convert the Percentage to a Decimal: A percentage means per 100. So we need to divide the number by 100 to convert it to a decimal.
[tex]\[
21 \frac{2}{3} \% = \frac{65}{3} \div 100
\][/tex]
4. Convert the Decimal to a Fraction: We then simplify the expression by dividing by 100:
[tex]\[
\frac{65}{3} \div 100 = \frac{65}{3 \times 100} = \frac{65}{300}
\][/tex]
5. Simplify the Fraction if Necessary: We need to check if the fraction can be simplified. For [tex]\(\frac{65}{300}\)[/tex]:
- The greatest common divisor (GCD) of 65 and 300 is 5.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{65 \div 5}{300 \div 5} = \frac{13}{60}
\][/tex]
So, the fraction that is equal to [tex]\(21 \frac{2}{3} \%\)[/tex] is [tex]\( \frac{13}{60} \)[/tex].
Therefore, the detailed solution shows that [tex]\(21 \frac{2}{3} \%\)[/tex] is equal to the fraction [tex]\(\frac{13}{60}\)[/tex] in its simplest form.
