Key ideas
- Best buy: use a table for each option and work down to the cost of one unit (1 gram, 1 litre, 1 item). This is the unitary method.
- Whatever you do to one column, do to the other. To get to 1, divide both columns by the same number.
- Change pounds to pence first if the cost of one unit would be very small.
- The lower cost for one unit is the better buy. Bigger is not always better!
- Finish with a written statement that quotes the numbers, like: Pack B is the better buy since 0.44p < 0.48p per gram.
- Currency: put the exchange rate in the top row of a table. Pounds → foreign: multiply (arrow on the left). Foreign → pounds: divide by the rate (arrow on the right).
- Money answers have 2 decimal places, like £64.66. Round to the nearest penny (or cent).
Pounds to euros (×)
| Pounds (£) | Euros (€) | |
|---|---|---|
| 1 | 1.16 | |
| 200 | 1.16 × 200 = 232 |
Euros to pounds (÷)
| Pounds (£) | Euros (€) | |
|---|---|---|
| 1 | 1.16 | |
| 58 ÷ 1.16 = 50 | 58 |
The exchange rates on this page are examples. Real rates change every day.
Best buy
Cereal is sold in two sizes. Box A: 500 g for £2.40. Box B: 750 g for £3.30. Which is the better buy? Give a reason for your answer.(3 marks)
Box A: work down to 1 gram.
Box A: 0.48p per gram✓1
Box A
| Weight (g) | Cost (p) | |
|---|---|---|
| 500 | 240 | |
| 1 | 240 ÷ 500 = 0.48 |
In plain EnglishChange £2.40 to 240p so the numbers are easier. Then divide both columns by 500 to get the cost of 1 gram.
Box B: work down to 1 gram.
Box B: 0.44p per gram✓2
Box B
| Weight (g) | Cost (p) | |
|---|---|---|
| 750 | 330 | |
| 1 | 330 ÷ 750 = 0.44 |
In plain EnglishSame again for Box B: £3.30 = 330p, then divide both columns by 750.
Compare and write a statement.
Box B is the better buy since 0.44p < 0.48p per gram. ✓3
In plain EnglishThe lower cost for one gram wins. Your statement must say which is better and quote both numbers.
⚠ No numbers, no mark. "Box B because it's cheaper" doesn't show anything. Always quote the two unit costs.
Best buy: per item
Cans of juice are sold in packs. A pack of 6 costs £3.90. A pack of 8 costs £4.96. Which pack is better value? Give a reason for your answer.(3 marks)
Cost of 1 can in each pack.
6-pack: 65p per can✓18-pack: 62p per can✓2
Pack of 6
| Cans | Cost (p) | |
|---|---|---|
| 6 | 390 | |
| 1 | 390 ÷ 6 = 65 |
Pack of 8
| Cans | Cost (p) | |
|---|---|---|
| 8 | 496 | |
| 1 | 496 ÷ 8 = 62 |
In plain EnglishWork down to one can in each table. Pence keeps the numbers whole.
Write a statement.
The pack of 8 is better value since 62p < 65p per can. ✓3
In plain EnglishLower cost per can is better value.
Changing pounds to another currency
Sam changes £350 into euros. The exchange rate is £1 = €1.16. How many euros does Sam get?(2 marks)
Set up the table.
| Pounds (£) | Euros (€) | |
|---|---|---|
| 1 | 1.16 | |
| 350 | ? |
In plain EnglishStart with the exchange rate on the top row: £1 is worth €1.16. Sam has £350, so that goes in the pounds column.
Multiply.1.16 × 350✓1= €406✓2
| Pounds (£) | Euros (€) | |
|---|---|---|
| 1 | 1.16 | |
| 350 | 1.16 × 350 = 406 |
In plain EnglishPounds to the foreign currency: multiply. Each pound is worth €1.16, so 350 pounds are worth 350 lots of 1.16.
Changing back to pounds
After her holiday, Mia has €290 left. She changes it back to pounds at £1 = €1.16. How many pounds does she get?(2 marks)
Set up the table.
| Pounds (£) | Euros (€) |
|---|---|
| 1 | 1.16 |
| ? | 290 |
In plain EnglishSame table, same rate. This time we know the euros and want the pounds.
Divide.290 ÷ 1.16✓1= £250✓2
| Pounds (£) | Euros (€) | |
|---|---|---|
| 1 | 1.16 | |
| 290 ÷ 1.16 = 250 | 290 |
In plain EnglishForeign currency back to pounds: divide by the rate. Check: you should get fewer pounds than euros, because each pound is worth more than a euro.
Check your answer: £250 × 1.16 = €290. ✓ Going forwards again gets you back to where you started.
Problems in context
A pair of trainers costs $85 in New York and £70 in Glasgow. The exchange rate is £1 = $1.25. Where are the trainers cheaper? Give a reason for your answer.(3 marks)
Change dollars to pounds.
85 ÷ 1.25✓1= £68✓2
| Pounds (£) | Dollars ($) | |
|---|---|---|
| 1 | 1.25 | |
| 85 ÷ 1.25 = 68 | 85 |
In plain EnglishTo compare, both prices must be in the same currency. Change the dollars into pounds: divide by the rate.
Compare and write a statement.
The trainers are cheaper in New York since £68 < £70. ✓3
In plain EnglishNow both prices are in pounds, so you can compare them and quote the numbers.
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Your turn
Calculator allowed. Show your tables in your jotter. Money answers: type the number, like 75.41 (you can leave out £, € or p). Stuck? Tap Need a hint?