GCSE Maths: Imperial units and currency (Foundation)
Part of the GCSE Maths units and compound measures chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Imperial units and currency
Most of the world uses metric units, but in the UK you will still meet imperial units: miles on road signs, pints of milk, pounds and stones for body weight, and feet and inches for height. You also need to change between different currencies when you go abroad, such as pounds (£) and euros (€). Both use the same idea: a conversion fact or rate that links the two units.
Facts that link imperial units
| Imperial facts (exact) | Approximate metric equivalents (often given in questions) |
|---|---|
| 12 inches = 1 foot 3 feet = 1 yard 1760 yards = 1 mile 16 ounces = 1 pound 14 pounds = 1 stone 8 pints = 1 gallon | 1 inch ≈ 2.5 cm 1 foot ≈ 30 cm 1 mile ≈ 1.6 km (5 miles ≈ 8 km) 1 kg ≈ 2.2 pounds 1 litre ≈ 1.75 pints 1 gallon ≈ 4.5 litres |
The ≈ sign means “is approximately equal to”. Between metric and imperial the conversions are only approximate, so answers are rounded sensibly.
The method
(1) Write the fact you are given, for example 1 mile ≈ 1.6 km. (2) Decide whether you need more or fewer of the target unit. A mile is longer than a km, so a distance in km is a bigger number: multiply by 1.6. To go back from km to miles you need fewer, so divide by 1.6. (3) Calculate and round sensibly. (4) Check by converting back.
Currency
An exchange rate tells you how much of one currency you get for one unit of another. If £1 = €1.15 then £200 gives 200 × 1.15 = €230. To change euros to pounds, divide by 1.15. Always round money to the nearest penny (or cent). If a question asks how much you need to buy something, check whether rounding up is more sensible.
Key ideas
- Always start by writing the conversion fact.
- Ask: will my answer be a bigger or smaller number? That tells you to multiply or divide.
- For a rate such as £1 = €1.15: £ to € multiply by 1.15; € to £ divide by 1.15.
- Round money to 2 decimal places.
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 inch ≈ 2.54 cm
- Decide: multiply or divide? The fact says 1 inch gives 2.54 cm, so the answer is 2.54 times the starting number: multiply by 2.54. The answer should be bigger than the number we started with.8 inches × 2.54
- Calculate. Use a calculator or work it out carefully.8 × 2.54 = 20.32
Check. Work backwards: 20.32 ÷ 2.54 ≈ 8. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 mile ≈ 1.6 km
- Decide: multiply or divide? The fact says 1.6 km make 1 mile, so the answer is the starting number shared into groups of 1.6: divide by 1.6. The answer should be smaller than the number we started with.56 km ÷ 1.6
- Calculate. Use a calculator or work it out carefully.56 ÷ 1.6 = 35
Check. Work backwards: 35 × 1.6 ≈ 56. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.16
- Decide: multiply or divide? The fact says 1 pound gives 1.16 euros, so the answer is 1.16 times the starting number: multiply by 1.16. The answer should be bigger than the number we started with.£250 × 1.16
- Calculate. Use a calculator or work it out carefully.250 × 1.16 = 290
Check. Work backwards: 290 ÷ 1.16 = 250. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.16
- Decide: multiply or divide? The fact says 1.16 euros make 1 pound, so the answer is the starting number shared into groups of 1.16: divide by 1.16. The answer should be smaller than the number we started with.€300 ÷ 1.16
- Calculate. Use a calculator or work it out carefully.300 ÷ 1.16 = 258.6207
- Round to 2 decimal places. The conversion fact is only approximate, so a sensible rounded answer is right.258.6207 ≈ 258.62
Check. Work backwards: 258.62 × 1.16 ≈ 300. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Change the stones into pounds, then add the extra pounds.
- Write the fact. The fact links stones and pounds exactly.1 stone = 14 pounds
- Change 3 stone to pounds. Stones are bigger than pounds, so multiply by 14.3 × 14 = 42 pounds
- Add the extra pounds. Do not forget the 4 pounds.42 + 4 = 46 pounds
Check. 46 ÷ 14 = 3 remainder 4, which is 3 stone 4 pounds. ✓
Watch out. Multiply only the stones by 14, then add the pounds.
Watch out
Do not just “times by the number”. Decide first whether the answer should be bigger or smaller. 100 euros is worth less than £100 here, so €100 in pounds must be a number smaller than 100: divide by the rate.Exercise 16D Imperial units and currency
Calculator allowedMethod. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 kg ≈ 2.2 pounds
- Decide: multiply or divide? The fact says 1 kilogram gives 2.2 pounds, so the answer is 2.2 times the starting number: multiply by 2.2. The answer should be bigger than the number we started with.5 kg × 2.2
- Calculate. Use a calculator or work it out carefully.5 × 2.2 = 11
Check. Work backwards: 11 ÷ 2.2 ≈ 5. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 inch ≈ 2.5 cm
- Decide: multiply or divide? The fact says 1 inch gives 2.5 cm, so the answer is 2.5 times the starting number: multiply by 2.5. The answer should be bigger than the number we started with.20 inches × 2.5
- Calculate. Use a calculator or work it out carefully.20 × 2.5 = 50
Check. Work backwards: 50 ÷ 2.5 ≈ 20. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 inch ≈ 2.5 cm
- Decide: multiply or divide? The fact says 2.5 cm make 1 inch, so the answer is the starting number shared into groups of 2.5: divide by 2.5. The answer should be smaller than the number we started with.150 cm ÷ 2.5
- Calculate. Use a calculator or work it out carefully.150 ÷ 2.5 = 60
Check. Work backwards: 60 × 2.5 ≈ 150. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 mile ≈ 1.6 km
- Decide: multiply or divide? The fact says 1 mile gives 1.6 km, so the answer is 1.6 times the starting number: multiply by 1.6. The answer should be bigger than the number we started with.30 miles × 1.6
- Calculate. Use a calculator or work it out carefully.30 × 1.6 = 48
Check. Work backwards: 48 ÷ 1.6 ≈ 30. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 mile ≈ 1.6 km
- Decide: multiply or divide? The fact says 1.6 km make 1 mile, so the answer is the starting number shared into groups of 1.6: divide by 1.6. The answer should be smaller than the number we started with.72 km ÷ 1.6
- Calculate. Use a calculator or work it out carefully.72 ÷ 1.6 = 45
Check. Work backwards: 45 × 1.6 ≈ 72. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 kg ≈ 2.2 pounds
- Decide: multiply or divide? The fact says 1 kilogram gives 2.2 pounds, so the answer is 2.2 times the starting number: multiply by 2.2. The answer should be bigger than the number we started with.10 kg × 2.2
- Calculate. Use a calculator or work it out carefully.10 × 2.2 = 22
Check. Work backwards: 22 ÷ 2.2 ≈ 10. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 kg ≈ 2.2 pounds
- Decide: multiply or divide? The fact says 2.2 pounds make 1 kilogram, so the answer is the starting number shared into groups of 2.2: divide by 2.2. The answer should be smaller than the number we started with.33 pounds ÷ 2.2
- Calculate. Use a calculator or work it out carefully.33 ÷ 2.2 = 15
Check. Work backwards: 15 × 2.2 ≈ 33. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 foot = 12 inches
- Decide: multiply or divide? The fact says 1 foot gives 12 inches, so the answer is 12 times the starting number: multiply by 12. The answer should be bigger than the number we started with.4 feet × 12
- Calculate. Use a calculator or work it out carefully.4 × 12 = 48
Check. Work backwards: 48 ÷ 12 = 4. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 foot = 12 inches
- Decide: multiply or divide? The fact says 12 inches make 1 foot, so the answer is the starting number shared into groups of 12: divide by 12. The answer should be smaller than the number we started with.60 inches ÷ 12
- Calculate. Use a calculator or work it out carefully.60 ÷ 12 = 5
Check. Work backwards: 5 × 12 = 60. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 yard = 3 feet
- Decide: multiply or divide? The fact says 1 yard gives 3 feet, so the answer is 3 times the starting number: multiply by 3. The answer should be bigger than the number we started with.3 yards × 3
- Calculate. Use a calculator or work it out carefully.3 × 3 = 9
Check. Work backwards: 9 ÷ 3 = 3. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 stone = 14 pounds
- Decide: multiply or divide? The fact says 1 stone gives 14 pounds, so the answer is 14 times the starting number: multiply by 14. The answer should be bigger than the number we started with.2 stone × 14
- Calculate. Use a calculator or work it out carefully.2 × 14 = 28
Check. Work backwards: 28 ÷ 14 = 2. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 pound = 16 ounces
- Decide: multiply or divide? The fact says 16 ounces make 1 pound, so the answer is the starting number shared into groups of 16: divide by 16. The answer should be smaller than the number we started with.48 ounces ÷ 16
- Calculate. Use a calculator or work it out carefully.48 ÷ 16 = 3
Check. Work backwards: 3 × 16 = 48. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.1 gallon = 8 pints
- Decide: multiply or divide? The fact says 8 pints make 1 gallon, so the answer is the starting number shared into groups of 8: divide by 8. The answer should be smaller than the number we started with.24 pints ÷ 8
- Calculate. Use a calculator or work it out carefully.24 ÷ 8 = 3
Check. Work backwards: 3 × 8 = 24. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.15
- Decide: multiply or divide? The fact says 1 pound gives 1.15 euros, so the answer is 1.15 times the starting number: multiply by 1.15. The answer should be bigger than the number we started with.£40 × 1.15
- Calculate. Use a calculator or work it out carefully.40 × 1.15 = 46
Check. Work backwards: 46 ÷ 1.15 = 40. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.15
- Decide: multiply or divide? The fact says 1 pound gives 1.15 euros, so the answer is 1.15 times the starting number: multiply by 1.15. The answer should be bigger than the number we started with.£225 × 1.15
- Calculate. Use a calculator or work it out carefully.225 × 1.15 = 258.75
Check. Work backwards: 258.75 ÷ 1.15 = 225. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.15
- Decide: multiply or divide? The fact says 1.15 euros make 1 pound, so the answer is the starting number shared into groups of 1.15: divide by 1.15. The answer should be smaller than the number we started with.€92 ÷ 1.15
- Calculate. Use a calculator or work it out carefully.92 ÷ 1.15 = 80
Check. Work backwards: 80 × 1.15 = 92. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = €1.15
- Decide: multiply or divide? The fact says 1.15 euros make 1 pound, so the answer is the starting number shared into groups of 1.15: divide by 1.15. The answer should be smaller than the number we started with.€172.50 ÷ 1.15
- Calculate. Use a calculator or work it out carefully.172.5 ÷ 1.15 = 150
Check. Work backwards: 150 × 1.15 = 172.5. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = $1.25
- Decide: multiply or divide? The fact says 1 pound gives 1.25 dollars, so the answer is 1.25 times the starting number: multiply by 1.25. The answer should be bigger than the number we started with.£64 × 1.25
- Calculate. Use a calculator or work it out carefully.64 × 1.25 = 80
Check. Work backwards: 80 ÷ 1.25 = 64. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = $1.25
- Decide: multiply or divide? The fact says 1.25 dollars make 1 pound, so the answer is the starting number shared into groups of 1.25: divide by 1.25. The answer should be smaller than the number we started with.$135 ÷ 1.25
- Calculate. Use a calculator or work it out carefully.135 ÷ 1.25 = 108
Check. Work backwards: 108 × 1.25 = 135. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Use the given fact to link the two units. To change into the unit with the bigger number multiply; to change back, divide.
- Write the conversion fact you are given. This tells us how the two units are linked. It is like an exchange rate.£1 = $1.25
- Decide: multiply or divide? The fact says 1 pound gives 1.25 dollars, so the answer is 1.25 times the starting number: multiply by 1.25. The answer should be bigger than the number we started with.£18.40 × 1.25
- Calculate. Use a calculator or work it out carefully.18.4 × 1.25 = 23
Check. Work backwards: 23 ÷ 1.25 = 18.4. ✓
Watch out. Multiplying and dividing are easy to mix up. Ask yourself: should my answer be a bigger or a smaller number than the one I started with?
Method. Find the cost in euros, then change to pounds by dividing by the rate.
- Cost in euros. 5 nights at €85 each.85 × 5 = €425
- Change euros to pounds. One pound buys 1.15 euros, so there are fewer pounds than euros: divide by 1.15.425 ÷ 1.15 = 369.5652
- Round to the nearest penny. Money has 2 decimal places.£369.57
Check. 369.57 × 1.15 ≈ 425.01, which is about 425. ✓
Method. Change one price into the other currency so you can compare, then find the difference.
- Change €540 to pounds. Euros to pounds: divide by 1.15.540 ÷ 1.15 = 469.5652 ≈ £469.57
- Compare the prices. Both are now in pounds.UK: £480 Spain: £469.57
- Find the difference. Subtract the smaller from the larger.480 − 469.57 = £10.43
Check. Check in euros: 480 × 1.15 = €552, which is more than €540. So Spain is cheaper. ✓
Method. Change one speed to the other unit, then compare.
- Write the fact. This links miles and kilometres.1 mile ≈ 1.6 km
- Change 30 mph to km/h. 30 miles in one hour is 30 × 1.6 km, so multiply by 1.6.30 × 1.6 = 48 km/h
- Compare. Both are now in km/h.48 km/h < 50 km/h, so 50 km/h is the higher limit.
Check. 50 km/h ÷ 1.6 = 31.25 mph, which is more than 30 mph. ✓
Method. Change ounces to grams, then compare with what Sue has.
- Write the fact. This links ounces and grams.1 ounce ≈ 28 g
- Change 8 ounces to grams. Each ounce is 28 g, so multiply by 28.8 × 28 = 224 g
- Compare. Is 200 g at least as much as the amount needed?224 g > 200 g, and 224 − 200 = 24 g short
Check. 200 g ÷ 28 ≈ 7.1 ounces, which is less than 8 ounces. ✓
Method. Think about which currency is worth more, then use the right operation.
- Compare the currencies. £1 buys €1.15, so one pound is worth more than one euro.€100 must be worth less than £100
- Spot the mistake. Dan got £115, which is more than £100. He multiplied when he should have divided.Euros to pounds: divide by 1.15
- Correct calculation. Divide by the rate and round to the nearest penny.100 ÷ 1.15 = 86.9565 ≈ £86.96
Check. 86.96 × 1.15 ≈ 100. ✓
Method. Take off the fee first, then convert what is left.
- Subtract the fee. The fee is taken before the exchange.300 − 6 = £294
- Convert to dollars. Pounds to dollars: multiply by 1.28.294 × 1.28 = $376.32
Check. $376.32 ÷ 1.28 = £294. ✓
Watch out. Convert the money after the fee is taken off, not before.
Method. Change stones to pounds and add the extra.
- Stones to pounds. 1 stone = 14 pounds, so multiply by 14.12 × 14 = 168 pounds
- Add the 6 pounds. Do not forget the extra pounds.168 + 6 = 174 pounds
Check. 174 ÷ 14 = 12 remainder 6. ✓
Method. Pounds to kilograms: divide by 2.2.
- Write the fact. This links kilograms and pounds.1 kg ≈ 2.2 pounds
- Divide. There are fewer kilograms than pounds.174 ÷ 2.2 = 79.0909
- Round to 1 d.p. The question asks for 1 decimal place.79.1 kg
Check. 79.1 × 2.2 ≈ 174. ✓