Direct proportion questions, worked from the unit rate
A direct proportion question gives you two amounts that change together at a constant rate, such as units and their cost, and asks for one of them at a new size. Find the rate for one unit, then multiply it by the new quantity, or divide a new cost by it to find how many units it buys.
Handing in the rate itself, or costing only the extra units instead of the whole order, answers a different question.
This drill gives you five untimed questions that each carry a supplier's invoice to a larger order, free to use with no sign-up, and each one is worked through after you submit.
5 questions · untimed · free to use · no sign-up
One question, worked from the price of one unit
Try the question before you read on. The first step finds the unit rate, which is what one unit costs, and the second carries it to the new quantity.
12 units cost 18 euros. At the same price per unit, what do 20 units cost?
- Find the unit rate, the price of one unit: 18 ÷ 12 = 1.50 euros.
- Multiply the unit rate by the new quantity: 1.50 × 20 = 30 euros.
Answer: 30 euros.
Check it forward: 30 ÷ 1.50 = 20 units at 1.50 euros each, the quantity the question asks about.
When the rate is not the same at both sizes
Direct proportion needs one price for every unit, at both quantities. A bulk discount that applies to one order size and not the other breaks that, and so does a fixed charge, such as delivery, that stays the same however many you order. Then cost the new quantity from the prices that apply to it. The questions in this drill all keep one price per filter, so this example sits here rather than in the set. Try it before you open the working.
The same supplier takes 10 percent off every unit on orders of 20 or more. What do the 20 units cost now?
Show the working
- The 1.50 euros comes from an order of 12, below the discount. At 20 units each unit costs 90 percent of that: 1.50 × 0.90 = 1.35 euros.
- Multiply the discounted rate by the quantity: 1.35 × 20 = 27 euros.
Answer: 27 euros.
A question in the drill's form
The drill's questions carry a supplier's invoice for filters to a larger order, with bigger figures than the ones above. This one is made the same way, with figures the drill itself does not use. Try it before you open the working.
A supplier invoices 600 euros for 40 filters. At the same price per filter, what does an order of 240 filters cost?
Show the working
- Find the price of one filter: 600 ÷ 40 = 15 euros.
- Multiply it by the whole order, not only the extra filters: 15 × 240 = 3,600 euros.
Answer: 3,600 euros. Testonome practice pace: 50 seconds for a question like this.
Check it forward: 3,600 ÷ 15 = 240 filters at 15 euros each, the order the question gives.
Four ways this question type goes wrong
Each question offers these alongside the right answer, and the review names which one you took.
Rate handed in
Stopping at the price of one unit, which is the first step rather than the answer.
Extra units only
Costing only the units beyond the first order, so the units already invoiced are left out of the total.
Rate upside down
Dividing the units by the price, which gives units per euro instead of euros per unit.
Units added as euros
Adding the extra units to the invoice as though each one cost a euro, which mixes a count with money.
What the review gives you after you submit
You get the working for every question, the answer you chose beside the right one, and the reason the option you picked is wrong. Nothing is sent anywhere while you work.
5 questions · untimed · free to use · no sign-up
Other numerical skills you can drill
The proportional scaling formula, beside the other numerical formulas