Fractions, decimals and
percentages: Working with percentages. 

3rd year of secondary education.  
Example 1.  
How to work out the percentage of a quantity. To work out the percentage of a quantity we express the percentage as a decimal and then multiply the quantity by this number. How to work out the percentage of a proportion. If we want to work out the percentage of a certain quantity, a, which is part of a whole C, we do the following:
 
 
Exercise 11 Work out:
a) 40% of € 580,000 Check your results in the window.  
Exercise 12 Work out what percentage: a) 6,320 is of 15,800 b) 96 is of 480 c) 16 is of 320 d) 750 is of 5,000 Use the formula given above and then check your answers in the window. 
Example 2.  
How to work out an increase in percentage: A book costs € 18. Its price increases by 12%. How much does it cost now? Increase: 18*0.12= €2.16 However, we could have just done the following: 18*(1+0.12)=18*1.12= €20.16 variation index >1+0.12=1.12 How to work out a decrease in percentage: A suit which cost € 252 is reduced by 25%. How much does it cost now? Reduction: 252*0.25= €63 However, we could also have just done the following: 252*(10.25)=252*0.75= €189 variation index >10.25=0.75  
 
Exercise 13 a) There are 184,300 unemployed people in a region. If this
number decreases by 19% how many unemployed people are there now? 
Example 3.  
How to work out consecutive increases and decreases in percentage: In 1990 the cost of living went up by 10% and by 8% in 1991. Then, in 1992 it went down by 5% (this data is not true). How much had the cost of living increased between 1990 and 1992? We have to imagine how the
price of something that cost €100 in January 1990 changed:
Therefore, the amount has increased by 12.86% (And not by 10+85=13%)  
Exercise 14 Over three decades an expanse of forest changes: from 1950 to 1960 it
increases by 28% By what percentage did the forest change between 1950 and 1980?  
Exercise 15 Over the period of a year the price of an article first increases by 40%, then decreases by 10% before finally decreasing a further 20%. Calculate the percentage change over the whole year. 
Example 4.  
How to work out the original amount if we know the percentage change and the final amount: A fridge costs € 336 after a price increase of 40%. What was the original price?
ORIGINAL PRICE = 336÷1.40= €240  
 
Exercise 16 In the sales we bought a painting for € 105, a bicycle for €50.40 and a book for €16.35. If all the prices were reduced by 30% how much would we have spent on the same items before the sales?  
Exercise 17 At a department store everything is reduced by 14%. These are the prices:

Ángela Núñez Castaín  
Spanish Ministry of Education. Year 2001  
Except where otherwise noted, this work is licensed under a Creative Common License