๐ What are Unit Rates?
A unit rate expresses a ratio as a quantity of 1. It tells you how much of something you get for a single unit of something else. Think of it as finding the price per item or the speed per hour.
๐ A Little Unit Rate History
The concept of rates and ratios has been around since ancient times! Early civilizations needed ways to compare quantities and measure proportions for trade, construction, and even calculating taxes. While the term 'unit rate' might be more modern, the underlying idea of comparing quantities relative to a single unit is an age-old practice.
๐ Key Principles for Calculating Unit Rates from Tables
- ๐ Understand the Table: Make sure you know what each row or column represents. What are the quantities being compared?
- โ Identify the Ratio: Determine the ratio you want to express as a unit rate (e.g., cost per item, distance per hour).
- calculate the Unit Rate: Divide the value of one quantity by the corresponding value of the other quantity to get a value of '1' for the denominator. For example, if $y$ is cost and $x$ is number of items, unit rate will be $\frac{y}{x}$.
- ๐ท๏ธ Label Your Answer: Always include the units in your answer (e.g., dollars per donut, miles per hour).
๐ก Real-World Examples
Example 1: Finding the Cost Per Item
A table shows the cost of different numbers of t-shirts:
| Number of T-shirts |
Cost |
| 3 |
$24 |
| 5 |
$40 |
To find the cost per t-shirt, divide the cost by the number of t-shirts:
- โ Using the first row: $24 / 3 = $8 per t-shirt.
- โ๏ธ Confirming with the second row: $40 / 5 = $8 per t-shirt.
Example 2: Calculating Speed
A table shows the distance traveled by a car over different amounts of time:
| Time (hours) |
Distance (miles) |
| 2 |
120 |
| 3 |
180 |
To find the speed (miles per hour), divide the distance by the time:
- ๐ Using the first row: $120 / 2 = 60$ miles per hour.
- โฑ๏ธ Confirming with the second row: $180 / 3 = 60$ miles per hour.
๐งช Practice Quiz
Solve the following unit rate problems:
- A table shows that 4 movie tickets cost $36. What is the cost per ticket?
- A baker uses 15 cups of flour to make 3 cakes. How much flour is needed for each cake?
- If a package of 8 batteries costs $12, what is the unit price per battery?
- Sarah reads 100 pages in 2 hours. How many pages does she read per hour?
- A car travels 250 miles on 10 gallons of gas. What is the car's mileage (miles per gallon)?
[Answer Key: 1. $9, 2. 5 cups, 3. $1.50, 4. 50 pages, 5. 25 mpg]
๐ Conclusion
Calculating unit rates from tables is a fundamental skill with wide-ranging applications. By understanding the principles and practicing with examples, you can easily find and interpret unit rates in various real-world scenarios!