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
b) 80% of 500
c) 5% of 250
d) 10% of 2,980
e) 20% of 5 million
f) 25% of 1 million
f) 30% of 3,000

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
New price: 18+2.16=
€20.16

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
New price: 252-63= €189

However, we could also have just done the following:

252*(1-0.25)=252*0.75= €189

variation index -->1-0.25=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?
b) A reservoir holds 340 hl of water. If this amount is reduced by 43% how much water is left in the reservoir?
c) The price of petrol has gone up by 5% this year. If it cost €0.799/litre at the start of the year how much does it cost 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:

 100®(+10%)®100*1.10=110 ¯ 110®(+8%)®110*1.08.08=118.8 ¯ 118.8®(-5%)®118.8*0.95=112.86

Therefore, the amount has increased by 12.86% (And not by 10+8-5=13%)

Exercise 14

Over three decades an expanse of forest changes:

from 1950 to 1960 it increases by 28%
from 1960 to 1970 it decreases by 40%
from 1970 to 1980 it increases by 15%

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:

 Trousers from € 80 to € 70.4 Are all the prices really reduced by 14%? Check that they are. Shirts from € 35 to € 30 Jumpers from € 54 to € 47.5 T-shirts from €12 to € 10 Jeans from € 96 to € 85

 Ángela Núñez Castaín Spanish Ministry of Education. Year 2001