6 pens for £3, or 10 pens for £4.50. The packs are different sizes, so the prices cannot be compared directly.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Bring both to one
Work out what a single pen costs in each pack. Now both are prices for the same thing.
With those two
£3 ÷ 6 = £0.50 each. £4.50 ÷ 10 = £0.45 each.
The comparison
£0.45 is less than £0.50, so the bigger pack is the better buy here.
Reduce both to the same unit
Is 3 kg for £7.50 better than 5 kg for £12? Find the price per kilogram: £2.50 and £2.40. The second is cheaper. Comparing "per one" is the only reliable way, because the packages are different sizes.
Either unit works
You could instead compare kilograms per pound: 0.4 and about 0.417. The second gives more per pound, so it is again the better buy. Both directions give the same conclusion, but you must remember which way is better — more per pound is good, more pounds per kilogram is not.
Cheapest is not always best
The larger pack is cheaper per kilogram but costs more overall, and if half of it spoils before you use it, it was not the better buy. Mathematics answers the question you asked; deciding which question to ask is your job.
A shortcut for close cases
If two packs have a simple size relationship — one twice the other — scale the smaller price up and compare directly. 3 kg for £7.50 scaled to 6 kg is £15, against 5 kg for £12 scaled to 6 kg by adding a fifth, £14.40. Sometimes scaling beats dividing.
Step 2: Try It Yourself
Set a price and a quantity, and read the cost of exactly one.
| Pens | Pounds |
|---|---|
| 6 | 3 |
| 12 | 6 |
Every row is the same ratio. 6 to 3 is the same comparison as 12 to 6.
Step 3: Watch an Example
One step at a time.
Watch Ana Choose a Pack
4 apples for £2, or 6 apples for £2.40.
- Step 1
She divides to get the first rate: 2 ÷ 4 = £0.50 an apple.
Step 4: Your Turn
Practice makes it stick.
The Juice Aisle
Problem 1 of 2
5 bottles cost £10. What is the price of one bottle, in pounds?
The Other Shelf
Problem 2 of 2
8 bottles cost £12. What is the price of one bottle, in pounds?
Price for One
1 of 4
3 kg for £9. Price per kg, in pounds?
2 of 4
4 kg for £10. Price per kg, in pounds?
3 of 4
Of those two, which is the better buy?
4 of 4
200 g for £4. Price per 100 g, in pounds?
Step 5: Quick Check
Show what you know.
Question 1 of 1
6 cakes for £9. Price for one, in pounds?
What You Learned
- Two different pack sizes cannot be compared by price alone.
- Divide to find the cost of exactly one of each.
- The smaller cost per one is the better buy.