To determine the unit rate when the denominator of a rate is 1, you essentially find out how much of the first quantity corresponds to just one whole of the second quantity. A unit rate is often helpful for comparing rates or understanding how much one unit of something costs or produces.
Example: 120 eggs from 20 chickens
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To find the unit rate, you divide the total quantity of eggs (120) by the total number of chickens (20):
\[ \text{Unit rate} = \frac{120 \text{ eggs}}{20 \text{ chickens}} = 6 \text{ eggs per chicken} \]
You can apply this method to the other problems to find their unit rates.
Let's go through the additional problems to identify the unit rate for each:
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$55 for 20 people
- To find the unit rate (cost per person), divide total cost by number of people: \[ \text{Unit rate} = \frac{55 \text{ dollars}}{20 \text{ people}} = 2.75 \text{ dollars per person} \]
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250 miles in 4 hours
- To find the unit rate (miles per hour), divide total miles by total hours: \[ \text{Unit rate} = \frac{250 \text{ miles}}{4 \text{ hours}} = 62.5 \text{ miles per hour} \]
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60 feet in 4 minutes
- To find the unit rate (feet per minute), divide total feet by total minutes: \[ \text{Unit rate} = \frac{60 \text{ feet}}{4 \text{ minutes}} = 15 \text{ feet per minute} \]
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48 books for 16 students
- To find the unit rate (books per student), divide the total number of books by the number of students: \[ \text{Unit rate} = \frac{48 \text{ books}}{16 \text{ students}} = 3 \text{ books per student} \]
In summary, a unit rate expresses how much of one quantity corresponds to a single unit of another quantity, and it can be easily calculated by dividing the total amount of the first quantity by the total amount of the second quantity. In the example of 120 eggs from 20 chickens, the unit rate tells you how many eggs each chicken lays on average. This concept is applicable across various scenarios, helping to simplify comparisons and understand ratios in everyday situations.