Theory
With successive percentage changes, the base changes after each step.
That is why you cannot simply add the percentages together.
Calculate the growth factor for each change. First multiply by the first growth factor and then use that intermediate value for the second change.
- Calculate the first growth factorConvert the first percentage change into a growth factor.
A growth factor tells you what to multiply the old value by.
No change corresponds to factor 1. You convert a percentage to a decimal number by dividing by 100.
For an increase, you add that decimal number to 1. For a decrease, you subtract it from 1.
- Divide the percentage by 100Divide the percentage by 100 to write it as a decimal number.
Dividing means sharing an amount fairly or seeing how many equal groups fit into it.
The first number is the total amount. The second number tells you what you divide by.
Always check whether the division works out exactly. If it does not, you get a decimal number or fraction as the answer.
- Subtract the decrease from 1For a decrease, the growth factor becomes less than 1.
- Divide the percentage by 100
- Apply the first changeMultiply the initial value by the first growth factor.
You use multiplication with equal groups.
A × B means that you take the same amount B, A times.Instead of adding again and again, you calculate the product all at once.
- Calculate the second growth factorConvert the second percentage change into a growth factor.
A growth factor tells you what to multiply the old value by.
No change corresponds to factor 1. You convert a percentage to a decimal number by dividing by 100.
For an increase, you add that decimal number to 1. For a decrease, you subtract it from 1.
- Divide the percentage by 100Divide the percentage by 100 to write it as a decimal number.
Dividing means sharing an amount fairly or seeing how many equal groups fit into it.
The first number is the total amount. The second number tells you what you divide by.
Always check whether the division works out exactly. If it does not, you get a decimal number or fraction as the answer.
- Subtract the decrease from 1For a decrease, the growth factor becomes less than 1.
- Divide the percentage by 100
- Apply the second changeMultiply the value after the first change by the second growth factor.
You use multiplication with equal groups.
A × B means that you take the same amount B, A times.Instead of adding again and again, you calculate the product all at once.
- Calculate the first growth factorCalculate the growth factor for the first change of 10%.
- Divide the percentage by 10010 ÷ 100 = 0,1.
- Add the increase to 11 + 0,1 = 1,1.
- Divide the percentage by 100
- Apply the first change100 × 1,1 = 110.
- Calculate the second growth factorCalculate the growth factor for the second change of 20%.
- Divide the percentage by 10020 ÷ 100 = 0,2.
- Subtract the decrease from 11 - 0,2 = 0,8.
- Divide the percentage by 100
- Apply the second change110 × 0,8 = 88.