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# Increasing by a percentage

**Percentages can be added**, whether they are in fraction, decimal or percentage form – however, the key is that what is being added must be in the same form. For example:

- In fraction form:

- Alternatively,
- Alternatively,

They can be added because they have the same common denominator of 100.

To **increase a number by a certain percentage**, find (100+that increase) percent of the original number.

For example, to increase a 2900 by 20%, we find 120% of 2900. Knowing that , we multiply , i.e.:

Note the decimal place hasn’t been inserted yet! As the question had a total of 1dp, we move the decimal place one to the left. So, the answer is 3480, the number 2900 increased by 20%.

# Decreasing a percentage

**Percentages can be subtracted** in the same way they can be added, for example:

- In fraction form:

To **decrease a number by a certain percentage**, find (100-that decrease) percent of the original number.

For example, to decrease 2900 by 30%, find 70% of 2900. As 70% is 0.7, we multiply , i.e.:

Note the decimal place hasn’t been inserted yet! As the question had a total of 1dp, we move the decimal place one to the left. So, the answer is 2,030, the number 2900 decreased by 30%.

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