1. RATES
A RATE is almost the same as a ratio except the units of the two quantities must be different.
Units are different!!
Example of a Rate:
Arthur runs 10 km every 2 hours.
(In words)

2. Writing Rates
Remember that you MUST include the units beside each term in your rate.
Fraction Forms
Ratio Form
10 km
2 h
10 km : 2 h
10 km / 2 h

3. Writing Rates
We often use the words “for every” or “per” when writing a rate in words.
10 km : 2 h
“10 km per 2 h” or
“10 km for every 2 h”

4. Writing Rates As a general rule: 1
When one of your units is money, this term should go FIRST in the rate. 2
When one of your units is time, this term should go LAST in the rate.

5. Examples Write the following rates in fraction form a)
Money! (should be 1st term) a)
$2 for every 20 apples.
$2 / 20 apples
Time! (should be 2nd term) b)
3 hours for every 200 km.
200 km / 3 h

6. Money! (should be 1st term)
Examples
Write the following rates in fraction form c)
5 births per 100 people.
5 births / 100 people
Money! (should be 1st term) d)
25 L of gasoline for every $26.
$26 / 25 L

7. UNIT RATES A UNIT RATE is a rate whose 2nd term must be 1.
2nd term is a 1
Example of a Unit Rate:
Liam walks 2 km every 1 hour. or
2 km/h
Liam walks 2 km per hour.

8. UNIT RATES Example of Unit Rates we see often: 100 km/h Speed limits
How far you can travel in 1 hour.
$1.06 / L
Unit prices
The price of 1 litre of gasoline.

9. The amount of mass in 1 mL of a substance
UNIT RATES
Example of Unit Rates we see often:
1 g/mL
Density
The amount of mass in 1 mL of a substance

10. Changing a Rate into a Unit Rate
If you are given a rate, how do you turn it into a unit rate which is the same value?
Answer:
Divide the 1st term by the 2nd term.

11. Changing a Rate into a Unit Rate
Examples: Convert these rates into Unit rates ÷
$5 / 20 apples
$0.25 / apple
The cost of 1 apple ÷
$9 / 8 L
$1.125 / L
The cost of 1 L of gasoline

12. Changing a Rate into a Unit Rate
Examples: Convert these rates into Unit rates ÷
220 km / 2 h
110 km/h
The distance travelled in 1 hour
Also, the speed of this vehicle!

13. Changing a Rate into a Unit Rate
Examples: Convert these rates into Unit rates ÷
$5.60 / 4 items
$1.40 / item
The cost of 1 item