Percentages
\(\frac{50}{100}\) is called 50 per cent and written 50% 
Conversions from Fractions or Decimals to Percentages
Examples

To emphasize the method outlined above
 Multiply the fraction by 100
 And solve using the rules of multiplication of fractions
If it is of any help, remember that
100 can be expressed as a fraction, in the form
\[ \frac{100}{1} \]
Conversions from Percentages to Fractions or Decimals
Conversion of Percentages to Fractions
To convert a percentage into a fraction, express the percentage as a fraction over 100, and then simplify to lowest terms, if possible
Examples

Conversion of Percentages to Decimal Numbers
To convert from a percentage to a decimal, just divide the percentage by 100.
Stated in an alternative but identical way, shift the decimal point two places to the left (remember that a number like 51 can be thought of as 51.0).
Examples


Finding percentages
Method

Examples
\[ 10\%\ \mbox{of } 50 = \frac{10}{100} \times 50 = \frac{1}{10} \times 50 = 5 \]\[ 10\%\ \mbox{of } 50 = 0.1 \times 50 = 5 \] 
 
\[48\% \ \mbox{of } 200 = \frac{48}{100} \times 200 = \frac{12}{25} \times 200 = 96\]\[ 48\% \ \mbox{of } 200 = 0.48 \times 200 = 96\] 
 
\[ 34\% \ \mbox{of } 120 = \frac{34}{100} \times 120= \frac{17}{50} \times 120 = 40.8\]\[ 34\% \ \mbox{of } 120 = 0.34 \times 120 = 40.8\] 

Increasing and Decreasing Percentages
Method

Examples
Step 1. Find \(1\%\) of the original amount \[ \frac{150}{100} = 1.5 \] Step 2. Find \(10\%\) of the original amount \[ 10\% = 15\] Step 3. Adding this to the original amount gives 165 
Step 1. Find \(1\%\) of the original amount \[ \frac{180}{100} =1.8\] Step 2. Find \(5\%\) of the original amount 

Discounts
In general, to find a percentage of a quantity, we could
 Divide the quantity by 100, to find 1%
 Multiply this 1% by whatever percentage we want to find, e.g. to find 65%, we would multiply by 65.
For example, to find 65% of £ 200
 Divide £ 200 by 100 to find that 1% of £ 200 is £ 2
 Multiply £ 2 by 65 to find that 65% of £ 200 is 130
In practise we can conflate these two operations into one operation, i.e.
Examples
Suppose we want to find 70% off a price of £ 235.
The reduction would be given by
= £ 164.50 Subtract this from the original price Question 1. What would be 70% off £ 534 ? 
Suppose we want to find 6% off a price of £ 685.
The reduction would be given by
= £ 41.10 Subtract this from the original price Question 2. What would be 8% off £ 893 ? 
Suppose we want to find 65% off a price of £ 174.
The reduction would be given by
= £ 113.10 Subtract this from the original price Question 3. What would be 65% off £ 132 ? 
Links to Other Sites
 All About Percentages and Ratios : links to about two dozen seperate areas.
 Percentages from mathgoodies
 Percentage Online Test
Questions from Past Papers
Kay has been given 4 labels to put on the sale rails at the clothes shop where she works.
1. Which label should she put on the trousers that are down from £ 24 to £ 16?
 A Label 1
 B Label 2
 C Label 3
 D Label 4
2. Which label should she put on the coats that are down from £ 50 to £ 35?
 A Label 1
 B Label 2
 C Label 3
 D Label 4
Liz runs an icecream stall. To check how popular each flavour is, she
records the number of each flavour sold.
1. Which icecream flavour sold only twothirds as many as toffee?
A Banana
B Strawberry
C Mint Choc Chip
D Tutti Frutti
2. What percentage of all the sales was the chocolate flavour?
A 7%
B 14%
C 28%
D 30%
3. Liz used 1 litre of vanilla icecream.
How much chocolate icecream did she use if all the icecreams were the
same size?
4. Additional data was recorded from a group of children who all had tutti frutti icecream. This made tutti frutti the unique mode for all the data. What is the minimum number of children in the group to give this statistic?
A 3
B 11
C 12
D 17
1. 120 people are invited to the Christmas Party at work. 10 were not able to come because they were doing other things. 20% of those left did not want to come. Of those who said they would 5 come had to cancel at the last minute.
How many people came to the party?
 A 81
 B 82
 C 83
 D 84
This year, a company makes a profit of £ 552 374
 In its report the company rounds this figure to the nearest £ 100 000, The rounded
figure is
 A £ 500 000
 B £ 550 000
 C £ 552 000
 D £ 600 000
 Next year the company expects to make 10% more profit than this year. Rounding to the
nearest £ 100 000 what is its expected profit for next year ?
 A £ 600 000
 B £ 607 000
 C £ 610 000
 D £ 660 000
40 000 people watched a football match. The total receipts for the match were £ 640 000.
 6500 of the people at the match were visiting supporters. What percentage of the people
watching the match were visiting supporters ?
 A 1.625%
 B 6.5%
 C 16.25%
 D 65%
 The visiting club is paid \(\frac{3}{8}\) of the match receipts. How much is the visiting club paid ?
 A £ 120 000
 B £ 240 000
 C £ 320 000
 D £ 400 000
 A 1.625%
 B 6.5%
 C 16.25%
 D 65%
 A £ 120 000
 B £ 240 000
 C £ 320 000
 D £ 400 000
Stage 3
A new clothing manufacturing company makes 32 000 items in its first year. The company plans to increase production by 8% per year.
a) How many items will be produced in the third year of operation?b) One of the employees says that the initial production figure will be doubled in the fifth year. Is this statement true?
Show how you would check the statement by using the formula
F = Final number of items produced
I = Initial number of items
p = percentage increase
t = time in years
c) The company is offered a contract to produce 60 000 items in the third year and needs to know the annual percentage increase required to achieve this target. Use the following formula to calculate the required annual percentage increase, p.
Stage 3
The population of Kenya has been increasing by 4.5% per year.
1) After how many years could you expect its population to have doubled ?2) Give two factors which could affect your forecast in part a
Stage 3
A community charity is allowed to reclaim VAT on some of the items it buys.
The charity buys 15 tables at £ 63.00 each, including VAT at 17.5%.
How much VAT might the charity reclaim altogether ?