Understanding Money: Pounds (£) and Pence (p)
In the United Kingdom, the currency is Pounds Sterling (£). One pound is made up of 100 pence (p).
£1 = 100p
When writing amounts of money:
- Amounts in pounds are usually written with the £ symbol before the number and two decimal places for the pence, e.g.,
£12.50(twelve pounds and fifty pence). - Amounts in pence can be written with the 'p' symbol after the number, e.g.,
75p. - When converting pence to pounds, divide by 100:
150p = £1.50. - When converting pounds to pence, multiply by 100:
£2.35 = 235p.
Basic Money Calculations
Calculations with money follow the same rules as decimal calculations. It's crucial to keep the decimal points aligned when adding or subtracting.
Adding Money
Example: You buy items costing £3.45, £0.80, and £12. What is the total cost?
Workings: Add column by column, keeping decimal points aligned.
Subtracting Money (Finding Change)
Example: You pay with a £20 note for items costing £16.25. How much change do you get?
Workings: Subtract, borrowing where necessary, keeping decimal points aligned.
Multiplying and Dividing Money
Multiplying Money
Example: 3 items cost £1.25 each. What is the total cost?
Calculation: £1.25 × 3
Answer: £3.75
Dividing Money (Sharing Costs)
Example: A bill of £45.60 is shared equally among 4 friends. How much does each pay?
Calculation: £45.60 ÷ 4
Answer: Each friend pays £11.40.
Percentages with Money (Discounts & Increases)
Calculating a Discount
Example: A T-shirt costs £20. It has a 15% discount. What is the sale price?
- Find the discount amount: 15% of £20.
(15 / 100) × £20 = 0.15 × £20 = £3.00. - Subtract the discount from the original price:
£20.00 - £3.00 = £17.00.
Answer: The sale price is £17.00.
Calculating a Price Increase (e.g., VAT)
Example: A service costs £150 before VAT. VAT is 20%. What is the total price including VAT?
- Find the VAT amount: 20% of £150.
(20 / 100) × £150 = 0.20 × £150 = £30.00. - Add the VAT to the original price:
£150.00 + £30.00 = £180.00.
Answer: The total price including VAT is £180.00.
Exam-Style Money Problems
1. Best Value
Shop A sells 6 apples for £1.80. Shop B sells 8 apples for £2.24. Which shop offers better value for money per apple?
Answer: Shop B offers better value.
Explanation:
- Shop A cost per apple:
£1.80 ÷ 6 = £0.30(or 30p) per apple. - Shop B cost per apple:
£2.24 ÷ 8 = £0.28(or 28p) per apple. - Since £0.28 is less than £0.30, Shop B offers better value per apple.
2. Savings Plan
Sarah wants to save £350 for a holiday. She saves £15.50 each week. How many full weeks will it take her to save enough money?
Answer: 23 weeks
Explanation:
- Divide the total amount needed by the weekly savings:
£350 ÷ £15.50. 350 ÷ 15.50 = 22.5806...- Since she needs to save the full amount, she will need 23 full weeks (as 22 weeks is not enough).
3. Overtime Pay
Tom works 35 standard hours a week at £12.00 per hour. Any overtime hours are paid at "time and a half" (1.5 times the standard rate). One week, Tom works 42 hours. Calculate his total pay for that week.
Answer: £546.00
Explanation:
- Standard pay:
35 hours × £12.00/hour = £420.00. - Overtime hours:
42 hours - 35 hours = 7 hours. - Overtime rate:
£12.00 × 1.5 = £18.00/hour. - Overtime pay:
7 hours × £18.00/hour = £126.00. - Total pay:
£420.00 + £126.00 = £546.00.
4. Comparing Hire Costs
Company A charges a £25 fixed fee plus £15 per day to hire a tool. Company B charges £20 per day with no fixed fee. For how many days of hire is Company B cheaper?
Answer: Company B is cheaper for hires of 1 to 4 days.
Explanation: Let 'd' be the number of days.
- Cost A =
£25 + (£15 × d) - Cost B =
£20 × d - Compare costs for different days:
- 1 day: A = £25+£15 = £40; B = £20. (B cheaper)
- 2 days: A = £25+£30 = £55; B = £40. (B cheaper)
- 3 days: A = £25+£45 = £70; B = £60. (B cheaper)
- 4 days: A = £25+£60 = £85; B = £80. (B cheaper)
- 5 days: A = £25+£75 = £100; B = £100. (Same cost)
- 6 days: A = £25+£90 = £115; B = £120. (A cheaper)
- So, Company B is cheaper for 1, 2, 3, or 4 days.
5. Calculating Profit Percentage
A shop buys a phone for £250 and sells it for £320. What is the percentage profit made on the phone?
Answer: 28%
Explanation:
- Calculate the profit amount:
Selling Price - Cost Price = £320 - £250 = £70. - Calculate the percentage profit:
(Profit / Cost Price) × 100%. - Percentage Profit =
(£70 / £250) × 100%. (70 / 250) = 0.28.0.28 × 100% = 28%.
Interactive Money Calculator (Discounts/Increases)
Amount of Change: ?
New Price: ?
Key Points for Money
- Remember
£1 = 100p. Be careful with conversions. - When adding or subtracting money, always align the decimal points.
- Percentage discounts reduce the price; percentage increases add to the price.
- "Best value" problems often require finding the cost per unit (e.g., cost per apple, cost per gram).