Rates
A rate compares two related quantities.
Often written as "this per that" but there are many possibilities, including a single number calculated using division.
Example: Sam makes 3 pancakes every 6 minutes
That's a rate of:
- 3 pancakes per 6 minutes
- 0.5 pancakes per minute
- 30 pancakes per hour
- an hourly rate of 30
- and so on
Example: 200 sausages were eaten by 50 people
That's
- 200 sausages per 50 people
- 100 sausages per 25 people
- 4 sausages per person
So the unit rate is 4 sausages per person.
Example: Alex invested $100 for a month and made $3
• the interest rate is 3/100 = 3% per month
Note: interest rates are usually quoted per year, but per month is also OK.
Unit Rate
When we compare to a single unit quantity we call it a Unit Rate.
Unit Rate: how much of something per 1 unit of something else.
Examples:
- 100 cars pass by in 2 hours. The unit rate is 50 cars per hour
- You can paint 3 boards in half an hour. The unit rate is 6 boards per hour
- 200 sausages were eaten by 50 people. The unit rate is 4 sausages per person
- They need 5 m of thread to make 2 cm of cloth. The unit rate is 2.5 m per cm
- The car can go 1000 km on 50 liters of fuel. The unit rate is 20 km per liter
- There are 100 students and 4 teachers. The unit rate is 25 students per teacher
- In the last 4 weeks Sam earned $2000. The unit rate is $500 per week
Which Way Do We Divide?
The order of division matters! It changes what our unit rate means.
Let's look at 3 pancakes in 6 minutes:
Divide Pancakes by Minutes:
3/6 = 0.5 pancakes per minute
(how fast we make them)
(how fast we make them)
Divide Minutes by Pancakes:
6/3 = 2 minutes per pancake
(how long each one takes)
(how long each one takes)
Ask yourself: "Do I want 'pancakes per minute' or 'minutes per pancake'?"
Unit Price
The Unit Price (or unit cost) tells us the cost per liter, per kilogram, per pound, and so on, of what we want to buy.
Rate vs Ratio
A rate compares different units (km per hour). A ratio compares the same kind of units (3 red to 2 blue).