A building has two sizes of apartments, small and regular. The ratio of small apartments to regular apartments is 11 to 9. What percent of apartments in the building are small?
Understand the Problem
The question is asking for the percentage of small apartments in a building based on the given ratio of small to regular apartments. We need to determine how the ratio relates to the total number of apartments and calculate the percentage of small apartments.
Answer
The percentage of apartments in the building that are small is \( 55\% \).
Answer for screen readers
The percentage of apartments in the building that are small is ( 55% ).
Steps to Solve
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Understand the Ratio The ratio of small apartments to regular apartments is given as ( 11:9 ). This means for every 11 small apartments, there are 9 regular apartments.
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Calculate Total Number of Apartments Add the parts of the ratio to find the total parts: [ \text{Total parts} = 11 + 9 = 20 ]
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Find the Fraction of Small Apartments The fraction of the building that consists of small apartments can be calculated by: [ \text{Fraction of small apartments} = \frac{11}{20} ]
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Convert Fraction to Percentage To convert the fraction to a percentage, multiply by 100: [ \text{Percentage of small apartments} = \left(\frac{11}{20}\right) \times 100 = 55% ]
The percentage of apartments in the building that are small is ( 55% ).
More Information
The calculation shows that out of every 20 apartments, 11 are small, leading to a significant proportion of smaller living spaces. This type of ratio is commonly used in real estate to understand the composition of structures.
Tips
- Failing to add the parts of the ratio correctly, which would lead to an incorrect total.
- Mistakenly flipping the ratio (confusing small with regular apartments) when calculating percentages.
- Forgetting to multiply by 100 when converting from a fraction to a percentage.
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