Revision notes
Recognise quantities in direct proportion and use the unitary method to scale prices, recipes and distances.
At the filling station, Chidi's dad buys petrol. 10 litres cost twice as much as 5 litres, and 20 litres cost four times as much. The price and the litres grow together — they are in direct proportion.
Two quantities are in direct proportion when doubling one doubles the other, tripling one triples the other, and so on.
Loaves of bread and their total cost are in direct proportion. So are hours worked (at a fixed rate) and pay.
But when more workers make a job take less time, that is inverse proportion — one goes up while the other goes down.
🔑 Key idea: Direct proportion: both quantities are multiplied by the same number.
Unitary means 'one'. First find the value of ONE, then multiply to get any number you want.
If 4 exercise books cost ₦1,000, then 1 book costs ₦1,000 ÷ 4 = ₦250, so 7 books cost 7 × ₦250 = ₦1,750.
To find how many you can buy, divide instead: ₦3,000 ÷ ₦250 = 12 books.
🔑 Key idea: Divide to find ONE, then multiply to find MANY.
A moi moi recipe uses 3 cups of beans for 6 people. For 1 person that is 3 ÷ 6 = 12 cup, so 10 people need 10 × 12 = 5 cups.
A car travels 60 km on 5 litres, which is 12 km per litre, so on 8 litres it goes 8 × 12 = 96 km.
Never just ADD the difference (6 people → 10 people is not '3 + 4 cups'). In direct proportion we always multiply.
🔑 Key idea: Scale by multiplying, never by adding.
4 bottles of water cost ₦2,000. How much do 2 bottles of water cost?
Step 1: Cost of 1 bottle of water
₦2,000 ÷ 4 = ₦500
Why? Finding the value of ONE first is called the unitary method.
Step 2: Cost of 2 bottles of water
2 × ₦500 = ₦1,000
Answer: ₦1,000
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.