3 Self-check on this unit
3.1 Self-check on percentages
Before starting the final badge activity, the following self-check activity will give you a chance to recap on what you have learned in this unit.
The more you practice, the more your skills improve. The exercises in this section will help you continue to develop your ability and check to make sure you understand the concepts discussed in this unit. Be sure to write your work out in your maths notebook so that you can refer to it later if necessary.
In this unit, you might have struggled with certain activities, and that’s OK! We all get stumped from time to time. Remember that there are plenty of resources that can provide guidance and advice, such as family, friends, teachers, old textbooks, and the Internet.
It’s important for you to reflect on the material you have studied and consider the development of your skills. Your confidence will continue to increase the more you practice. You can do this by working through the exercises for each section. Here are some activities to help you perform a self-check.
Exercise 1 Fractions, decimals and percentages
Copy the table below into your notebook. Then, fill in the columns to show which fractions, decimals, and percentages are equivalent to each other. You have worked out some of these calculations already earlier in this unit.
| Percentage | Decimal | Fraction |
|---|---|---|
| 5% | 0.05 |  |
| 10% | ||
| 0.2 | ||
 | ||
 | ||
| 0.5 | ||
 | ||
| 75% | ||
| 1 |
Comment
To change a fraction or decimal to a percentage, multiply it by 100 per cent.
For example, 
and 
.
To change a percentage to a fraction or decimal, interpret the % symbol to mean ‘divided by 100’.
For example, 
and 
.
To change a fraction to a decimal, divide the numerator by the denominator.
For example: 
.
Answer
| Percentage | Decimal | Fraction |
|---|---|---|
| 5% | 0.05 |  |
| 10% | 0.1 |  |
| 20% | 0.2 |  |
| 25% | 0.25 |  |
| 30% | 0.3 |  |
| 50% | 0.5 |  |
| 64% | 0.64 |  |
| 75% | 0.75 |  |
| 100% | 1 | 1 |
Note: converting a decimal into percentage means moving the decimal point two places to the right and including the per cent symbol.
Note: in your conversion from a fraction to a percentage you can also go through the decimal, i.e. work out the quotient and then move the decimal point two places to the right and include the per cent symbol.
Exercise 2a Hotel room
A hotel in Milton Keynes has rooms available for £56.80 per person for one night. If the hotel applies a 10 per cent surcharge for one person occupying a double room, what is the total cost of a double room with single occupancy for one night?
Answer
10 per cent of £56.80 is £5.68. Then, add the service charge to the room cost, 
. The total cost of the room is £62.48.
Exercise 2b Sales figures
In January, a company sells £8500 worth of goods. However, the sales fall by 8 per cent in February. How much is sold in February?
Answer
8 per cent of £8500 is 
.
The total sales in February are 
.
Alternatively, 92 per cent of £8500 is 
.
Exercise 2c VAT
An item costs £35.49, excluding VAT . If VAT is 20 per cent, what is the total price?
Answer
20 per cent of £35.49 is £7.10 in VAT. Together it is 
.
The item costs £42.59 after VAT.
Alternatively, 
.
Exercise 3 A clerical error
A mail order company offers a 15 per cent reduction on its prices to new customers. Unfortunately, a clerical error has been made and some existing customers have also been given the discount. One existing customer has been charged £144.50, including the discount. What should the customer have been charged? How can you check your answer?
Answer
The reduction is 15 per cent, so eligible customers are charged 85 per cent of the original cost. 85 per cent of the cost is £144.50.
1 per cent of the cost is 
and 100% of the cost is 
.
The existing customer should have been charged £170.
You can check this answer by calculating the reduced price: 15 per cent of £170 is 
. So the reduced price is 
.
Exercise 4 Large group at a restaurant
You and six friends went out to dinner together – a party of seven in all. The restaurant’s policy stated that groups of six people or more will have an 18 per cent tip added to their bill. If your food and drinks totalled £176.23, how much was the bill? If you had split the bill evenly seven ways, how much was your share?
Answer
18% of 176.23 is 
and the total bill was 
.
Divide by seven and 
is what everyone owed.
Exercise 5 ‘Of’ versus ‘off’
(a) What percentage of the original price do you pay if an ad promises ‘20 per cent off everything?’
Answer
You pay 80 per cent of the original price.
(b) What percentage of the original price do you pay if ‘the sale price is 40 per cent of the original price?’
Answer
You pay 40 per cent of the original price.
Exercise 6 Discount
Find the sale price of a £340 television that is on sale for 25 per cent off.
Answer
25% of £340 is 
. With a discount of £85, the sales price of the television is 
.
Exercise 7 Time for that new television
The price of a 55-inch flat-screen HD television is £1897, which includes 20 per cent VAT. How much did the television cost before VAT was added?
Answer
£1897 is 120 per cent of the original price. Dividing the shop price by 120 per cent gives you 1 per cent of the original price: £1897 ÷ 120 = £15.81 (to the nearest penny). Multiply this result by 100 to create 100%, and thus the original price, which is 
(rounded to the nearest penny).
The pretax price of the television was £1580.83. You can check your answer by finding out what a television of 1580.83 would cost after 20% VAT is applied.
Exercise 8 Spending
The UK Office of National Statistics calculates and published weekly expenditure figures each year. For 2011, the total average weekly expenditure was £483.60; of this, £21.70 was spent on clothing and footwear, £39.70 on restaurants and hotels, £54.80 on food and soft drinks, and £65.70 on transport.
Calculate what percentage of the total average weekly expenditure each of these categories account for.
Answer
- Clothing and footwear:
- Restaurants and hotels:
- Food and soft drinks:
- Transport:
