Grade 8 · Math · Unit 6 of 18
Ratios, Rates & Proportions
Unit rates, best buys and scale
What your child practises
Simplifying ratios, finding missing terms in equivalent ratios, comparing unit prices, working with speed, scaling recipes and map distances, and turning a part of a whole into a percent.
Ontario Curriculum expectation: B2.8 · ratios, rates and proportional reasoning
How we explain it
Children can open this short lesson before they practise.
- A ratio compares two amounts, like 2 : 3.
- A rate compares different units, like dollars per pen.
- A unit rate is the amount for 1: divide to find it.
Example: 6 pens cost $4.50. What is the price for 1 pen? Divide the cost by the number of pens. 4.50 ÷ 6 = 0.75. Answer: $0.75 per pen
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A bag has 20 red marbles and 12 blue marbles. What is the ratio of red to blue in lowest terms?
- 5:8
- 5:3
- 3:5
- 20:12
- 6:4
Show answer
5:3
Hint: Divide both parts by their greatest common factor, 4: 20 ÷ 4 = 5 and 12 ÷ 4 = 3.
Question 2
7 : 8 = 35 : ?
answer box
Show answer
40
Hint: 7 was multiplied by 5 to get 35, so multiply 8 by 5 too: 8 × 5 = 40.
Question 3
4 notebooks cost $3.40. What is the price of one notebook, in dollars?
answer box
Show answer
0.85
Hint: Divide the total by the number of notebooks: $3.40 ÷ 4 = $0.85.
Question 4
A cyclist rides 320 km in 5 hours at a steady pace. What is the speed in km per hour?
answer boxkm/h
Show answer
64 km/h
Hint: Speed is distance ÷ time: 320 ÷ 5 = 64 km/h.
Question 5
Pack A: 4 juice boxes for $0.80. Pack B: 12 juice boxes for $2.64. Which pack is the better buy?
- Pack A
- They cost the same per box
- Pack B
Show answer
Pack A
Hint: Compare the price per box: Pack A is about 0.20 each and Pack B is about 0.22 each. The lower unit price is the better buy.
Question 6
A recipe for 6 people uses 6 cups of rice. How many cups are needed for 30 people?
answer boxcups
Show answer
30 cups
Hint: 30 people is 5 times as many as 6, so use 5 times the rice: 6 × 5 = 30 cups.