Ratios & Rates
Extend your understanding of ratios to include unit rates, scale drawings, and speed-distance-time problems.
From Ratios to Rates
A ratio compares two quantities of the same kind (e.g. boys to girls). A rate compares two quantities of different kinds (e.g. kilometres per hour, dollars per kilogram).
Ratio
3 red : 5 blue (same kind — colours)
Rate
60 km in 1 hour (different kinds — distance & time)
Unit Rate = total amount ÷ number of units
A unit rate tells you how much per one unit.
$12 for 4 kg of apples. What is the unit rate?
Step 1: $12 ÷ 4 kg = $3 per kg
Answer: $3/kg
Scale Drawings
A scale tells you how a drawing relates to real life. For example, a scale of 1 : 100 means 1 cm on the drawing equals 100 cm (1 m) in real life.
A floor plan uses a scale of 1 : 200. A room is 5 cm on the plan. What is the real length?
Step 1: Real length = drawing length × scale factor
Step 2: 5 cm × 200 = 1,000 cm = 10 m
Answer: 10 metres
Speed, Distance & Time
Speed is a rate that compares distance to time.
Speed
= Distance ÷ Time
Distance
= Speed × Time
Time
= Distance ÷ Speed
A car travels 240 km in 3 hours. What is its speed?
Step 1: Speed = Distance ÷ Time
Step 2: Speed = 240 ÷ 3 = 80 km/h
Knowledge Check
Select the correct answer for each question. Questions get harder as you go!
Question 1
6 oranges cost $3. What is the cost per orange?
Question 2
A car travels 150 km in 2 hours. What is its speed?
Question 3
On a map with scale 1 : 1,000, a path measures 4 cm. How long is the real path in metres?
Question 4
Which is the better buy: 5 kg for $10 or 3 kg for $7.50?
Question 5
A cyclist travels at 20 km/h. How far will they travel in 2.5 hours?
Question 6
A real building is 15 m tall. On a scale model at 1 : 50, how tall is the model?
Question 7
A train covers 360 km at a speed of 90 km/h. How long does the journey take?
Question 8
Mia earns $84 for 7 hours of work. Josh earns $65 for 5 hours. Who has the higher hourly rate, and by how much?
Question 9
A car leaves town A at 80 km/h. Another leaves town B (200 km away) at the same time, heading towards A at 120 km/h. After how long do they meet?
Question 10
A model car is 8 cm long and the real car is 4 m long. What is the scale of the model?
Key Concepts Summary
- ●A rate compares quantities of different kinds (e.g. $/kg, km/h).
- ●A unit rate tells you the amount per one unit.
- ●Scale = model : real. Convert to the same units before simplifying.
- ●Speed = Distance ÷ Time. Rearrange to find distance or time.