# 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, $200\%+60\%=260\%$
• Alternatively, $2.00+0.6=2.6$

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 $120\%=1.2$, we multiply $1.2*2900$, 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: • $300\%-90\%=210\%$
• $0.300-0.9=2.1$

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 $0.7*2900$, 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%.