Rates and Average
Grade 8 math lesson on rates and averages including unit rates, average speed, and rate calculations. Students learn to calculate rates by dividing a quantity by time or another unit, and find averages by summing values and dividing by the count.
Key Concepts
Property A rate is a division relationship between two measures, often expressed as a unit rate like miles per hour. You can use rates to find a total amount, or use total amounts to find the rate itself.
Examples Heather biked 100 km in 4 hours. Her average speed was $\frac{100 \text{ km}}{4 \text{ hr}} = 25$ kilometers per hour. Driving for 6 hours at an average speed of 55 mph, the total distance is $6 \text{ hours} \times 55 \text{ mph} = 330$ miles.
Explanation Rates make comparing things a snap by boiling them down to a "per one" basis. To find a rate, like average speed, you simply divide the total distance by the total time. This trick works for prices, speeds, and so much more, helping you become a savvy problem solver!
Common Questions
What is a rate in math?
A rate is a ratio that compares two quantities with different units. Common rates include speed (miles per hour), price (dollars per pound), and pay (dollars per hour). Rates are written as one quantity divided by another.
How do you calculate average speed?
Average speed equals total distance divided by total time. For example, if you travel 120 miles in 2 hours, your average speed is 120 / 2 = 60 miles per hour.
What is an average and how do you calculate it?
An average (arithmetic mean) is found by adding all values in a data set and dividing by the number of values. For example, the average of 10, 20, and 30 is (10+20+30)/3 = 20.
What is the difference between a rate and a ratio?
A ratio compares two quantities of the same type (like 3 apples to 5 oranges). A rate compares two quantities of different types (like 60 miles per 1 hour). Rates always include different units.