# Percentages » Calculating faster with percentages

## Contents

1. How much is 4.5 per cent of 800?2. What percentage is 18 of 80?

3. What percentage do you increase from 12 to 15?

4. What percentage do you decrease from 15 to 12?

5. Growth factors

6. Calculate back to the original

7. More examples

## Per cent or percent or percentage?

British spelling uses 'per cent'.

American spelling uses 'percent'.

Both use 'percentage'.

## 1. How much is 4.5 per cent of 800?

Per cent means 'per one hundred'. You may also read this as 'of the one hundred'.

So we need 4.5 of the one hundred of 800.

4.5 of the one hundred is 4.5/100 = 0.045. You can see, that the decimal dot moves two places to the right.

So you can write 4.5/100 × 800 or 0.045 × 800 as your calculation.

*Examples*

12% of 40 = 0.12 × 40 = 4.8

70% of 90 = 0.7 × 90 = 63

140% of 75 = 1.4 × 75 = 105

17.5% of 66 = 0.175 × 66 = 11.55

## 2. What percentage is 18 of 80?

The fastest way of calculating a percentage is using the following rule.

`percentage` = `amount``total` × 100%

To make the calculation correct you also have to write the %-sign behind the 100. However, you do not key this %-sign in on your calculator. For that reason I have written the %-sign in red. However, you do not use a different colour for this %-sign. It is only used here to explain this point.

*Examples*

18 of 80 = 18 : 80 × 100% = 22.5%

37.8 of 270 = 37.8 : 270 × 100% = 14%

15 of 300 = 15 : 300 × 100% = 5%

## 3. What percentage do you increase from 12 to 15?

### Method 1: Use a growth factor:

`growth factor` = `new``old`

With the growth factor you calculate what the percentage increase must have been.

*Examples*

Event | Calculation |

from 12 to 15 | 15 : 12 = 1.25. Increase was 25% |

from 125 to 145 | 145 : 125 = 1.16. Increase was 16% |

from 24 to 25.56 | 25.56 : 24 = 1.065. Increase was 6.5% |

### Method 2: Without the use of a growth factor:

`percentage increase` = `new` – `old``old` × 100%

*Examples*

Event | Calculation |

from 12 to 15 | (15 – 12)/12 × 100% = 25% |

from 125 to 145 | (145 – 125)/125 × 100% = 16% |

from 24 to 25.56 | (25.56 – 24)/24 × 100% = 6.5% |

## 4. What percentage do you decrease from 15 to 12

You can just use the rules that are given at point 3 above.

### Method 1

With method 1, you will get a growth factor between 0 and 1.

*Examples*

Event | Calculation |

from 15 to 12 | 12 : 15 = 0.8. Decrease was 20% |

from 60 to 51 | 51 : 60 = 0.85. Decrease was 15% |

from 96 to 64.8 | 64.8 : 96 = 0.675. Decrease was 32.5% |

### Method 2

With method 2, you will get a negative increase (which is a decrease).

*Examples*

Event | Calculation |

from 15 to 12 | (12 – 15)/15 × 100% = –20%. So a decrease of 20% |

from 60 to 51 | (51 – 60)/60 × 100% = –15%. So a decrease of 15% |

from 96 to 64.8 | (64.8 – 96)/96 × 100% = –32.5%. So a decrease of 32.5% |

## 5. Growth factors

For a technical explanation, check growth factors.

*Examples*

Event | Calculation |

30 increases with 15% | 30 × 1.15 = 34.5 |

30 increases with 215% | 30 × 3.15 = 94.5 |

30 decreases with 5% | 30 × 0.95 = 28.5 |

30 decreases with 0.2% | 30 × 0.998 = 29.94 |

## 6. Calculate back to the original

The fastest way to do this is, is by using growth factors again.

If you find that difficult, you can always use a percentages ratio table.

*Example 1*

Something has been reduced in price by 13% and costs 30.45 euros. What was the original price?

The old amount is multiplied with 0.87 to get 30.45.

We only have to calculate back: 30.45 : 0.87 = 35 euros.

*Example 2*

An amusement park had 17% more visitors in 2010 than in the year before.

In 2010 the park had 49 633 visitors. How many visitors did the park have in 2009?

The number of visitors in 2009 multiplied by 1.17 is the number of visitors in 2010.

Calculating backwards gives: 49 633 : 1.17 = 42 421 (rounded to a whole visitor)

## 7. More examples

*Example 1*

A sweater is being sold with a reduction of 20% for only 39.95 euros.

What was the original price of the sweater?

Answer:

39.95 : 0.8 = 49.94

*Example 2*

Bob borrows 1500 euros from the bank.

Every month he has to pay 1% interest.

How much interest has Bob paid after 6 months?

Answer:

1500 × 0.01 × 6 = 90 euros.

*Example 3*

Els puts 1500 euro in a savings account at the bank.

Every month she receives 1% interest on that amount.

How much interest has Els gotten after 6 months.

Answer:

Because Els is receiving interest on interest the answer cannot be so simply calculated as in example 2.

Her savings amount is increasing with 1% so that is a growth factor of 1.01.

After 6 months she has 1500 × 1.01^{6} ≈ 1592.28 in her account.

So she has received 1592.28 – 1500 = 92.28 euros interest.

*Example 4*

In a big pond are 180 gold fishes and 250 gold minnows.

A heron comes and eats 5% of the gold fishes and 12% of the gold minnows.

What percentage of fish disappeared from the pond?

If necessary, round to one decimal.

Answer:

180 + 250 = 430 fish in total

180 × 0.05 + 250 × 0.12 = 39 fish were eaten

39 : 430 × 100% ≈ 9.1% disappeared