Unit Rate
A unit rate is a rate in which the second term is 1. It is often used to compare different quantities or to find and compare prices.
For example, if a car travels 300 miles in 5 hours, the unit rate would be 300 miles per 5 hours, or 60 miles per hour. This means that the car is traveling at an average speed of 60 miles per hour.
Similarly, if a computer is priced at $800 and it can be purchased with a 20% discount, the unit rate would be $800 per 1 computer. This means that the price of one computer is $800.
Unit rates are useful for comparison purposes as they allow us to easily compare different quantities or prices on a per-unit basis. They can also be used to find the cost or value of a single unit when given the total quantity or price.
Unit rate is a comparison of two quantities in a ratio where the denominator is always 1. It is used to determine the rate of change of one quantity with respect to another quantity.
To find the unit rate, you divide the given quantity by the corresponding quantity of interest. For example, if you are trying to find the unit rate of speed, you would divide the distance traveled by the time it took to travel that distance.
Here is an example to help illustrate how to find the unit rate:
Suppose you traveled a distance of 120 miles in 2 hours. To find the unit rate of your speed, you would divide the distance (120 miles) by the time (2 hours):
Unit Rate of Speed = Distance / Time
= 120 miles / 2 hours
= 60 miles per hour
So, the unit rate of your speed is 60 miles per hour, which means you were traveling at an average rate of 60 miles per hour.
A unit rate is a comparison of two different quantities, where one quantity is compared to a single unit of the other quantity. It expresses the rate of change or relationship between the two quantities.
To find the unit rate, you need to determine the relationship between the given quantities and express it as a ratio. Then, simplify the ratio to make sure it is written with a denominator of 1.
Here's a step-by-step process to find the unit rate:
1. Identify the given quantities: Determine which two quantities are being compared. For example, let's say we are comparing the distance traveled and the time taken.
2. Write the comparison as a ratio: Express the relationship between the quantities by writing one number as the numerator of the ratio and the other number as the denominator. For example, if the distance traveled is 50 miles and the time taken is 2 hours, the ratio would be 50 miles / 2 hours.
3. Simplify the ratio: To express the unit rate, simplify the ratio so that the denominator is 1. This means dividing both the numerator and denominator by the same value until the denominator becomes 1. In our example, if we divide 50 miles and 2 hours by 2, the simplified ratio becomes 25 miles / 1 hour.
4. Interpret the unit rate: The simplified ratio 25 miles / 1 hour represents the unit rate, which means that the object or person is traveling at a rate of 25 miles per hour.
In summary, a unit rate compares two quantities by expressing their relationship as a ratio, which is then simplified to have a denominator of 1. The unit rate provides a standardized way to compare values and understand the rate of change between them.