Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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.
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.
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.