Understanding Rate
Learn what rate means and how to calculate it using division and multiplication
1. What is Rate?
Definition:
A rate tells us how much of one quantity there is for every one unit of another quantity.
The Word "Per":
"Per" means "every" or "for each"
📄 50 pages per minute
= 50 pages every minute
💵 $15 per hour
= $15 for each hour
🚗 80 km per hour
= 80 km every hour
💧 2 litres per hour
= 2 litres for each hour
Real-life examples: Speed of a car, price per item, words typed per minute, water collected per hour — these are all rates!
2. Finding the Rate (Unit Rate)
Key Idea:
To find the rate, we divide to find how much for 1 unit.
Using a Rate Table:
A photocopier takes 5 minutes to print 300 pages. How many pages does it print per minute?
| 5 min | 300 pages |
| 1 min | ? pages |
Solution:
Since we divide 5 min by 5 to get 1 min, we also divide 300 pages by 5.
300 ÷ 5 = 60
The photocopier prints 60 pages per minute.
More Examples:
Example 1: Distance
A robot walks 20 m in 4 minutes. How far does it walk in 1 minute?
20 m ÷ 4 = 5 m per minute
Example 2: Money
Mark is paid $75 for working 5 hours. What is the rate of his pay per hour?
$75 ÷ 5 = $15 per hour
Example 3: Water
12 litres of water was collected from a dripping tap in 6 hours. How much water was collected per hour?
12 ℓ ÷ 6 = 2 ℓ per hour
3. Using Rate to Calculate
Key Idea:
When we know the rate and want to find a larger amount, we multiply.
Example: Using Rate to Find Total
Miriam is paid $11 an hour for working at a restaurant. How much is she paid for working 10 hours?
| 1 h | $11 |
| 10 h | $? |
Solution:
Since we multiply 1 h by 10 to get 10 h, we also multiply $11 by 10.
$11 × 10 = $110
Miriam is paid $110 for working 10 hours.
Another Example:
In 2 hours, Susan cycles 58 km. At this rate, how far can she cycle in 6 hours?
| 2 h | 58 km |
| 6 h | ? km |
Solution:
Since 2 h × 3 = 6 h, we multiply 58 km by 3.
58 km × 3 = 174 km
She can cycle 174 km in 6 hours.
4. Two-Step Rate Problems
Strategy:
Sometimes we need to:
Step 1: Find the unit rate (÷)
Step 2: Then calculate the target amount (×)
Example: Wheel Revolutions
A wheel can make 42 revolutions in 3 minutes. At this rate, how many revolutions can it make in 7 minutes?
| 3 min | 42 revolutions |
| 1 min | ? revolutions |
| 7 min | ? revolutions |
Step 1:
Find revolutions per minute 42 ÷ 3 = 14 revolutions per minute
Step 2:
Find revolutions in 7 minutes 14 × 7 = 98 revolutions
The wheel can make 98 revolutions in 7 minutes.
Example: Construction Work
A construction worker lays 8 m² of tiles every 30 minutes. At this rate, what is the floor area he can lay with tiles in 2 hours?
Note: 30 min is half an hour, so here we multiply by 2 to find the rate for 1 hour.
Step 1:
Find the area tiled in 60 min (1 hour) 30 min × 2 = 60 min, so 8 m² × 2 = 16 m² per hour
Step 2:
Find the area tiled in 2 hours 16 m² × 2 = 32 m²
He can lay 32 m² of tiles in 2 hours.
Practice Problems
Practice 1: Finding Rate
A printer prints 36 pages in 4 minutes. At this rate, how many pages does it print per minute?
ShowHide solution
36 ÷ 4 = 9 pages per minute
Practice 2: Using Rate
A shopkeeper sells cloth at $9 per metre. Shanti buys 15 m of cloth. How much does she pay for the cloth?
ShowHide solution
$9 × 15 = $135
Practice 3: Rate per Hour
A machine packs 9600 bottles into boxes every 5 hours. At this rate, how many bottles does it pack into boxes per hour?
ShowHide solution
9600 ÷ 5 = 1920 bottles per hour
Practice 4: Distance Problem
A car travels 450 km in 5 hours. At this rate, how far can it travel in 8 hours?
ShowHide solution
Step 1:
Find rate per hour 450 ÷ 5 = 90 km per hour
Step 2:
Find distance in 8 hours 90 × 8 = 720 km
Key Takeaways
- Rate tells us how much for every one unit (e.g., pages per minute, $ per hour)
- "Per" means "every" or "for each"
- To find the rate: divide to find how much for 1 unit
- To use the rate: multiply to find larger amounts
- For two-step problems: first find the unit rate (÷), then calculate the target (×)
- Use a rate table to organise your working