Multistep percentage questions change the base at each step, and that is where most errors enter. This series belongs to consumer mathematics and financial planning, and all offers in it are invented.
Why do two percentages not simply add?
Take an item marked at RM100. A 20% discount leaves RM80, and a further 10% off RM80 is RM8, which leaves RM72.
The total reduction is RM28, which is 28% of RM100. It is not 30%, because the second 10% was taken from RM80, not from RM100.
What are the four lessons?
Each lesson targets one trap.
- Recovering an original amount after successive percentage changes
- Distinguishing percentage points from a percentage change
- Comparing instalment totals using supplied fees
- Explaining why a larger discount percentage can still give a higher amount to pay
Who should start where?
If you work backwards from a final amount and get the wrong original, start with lesson 1. If statements about rates confuse you, start with lesson 2.
If you choose plans by the smallest monthly payment, read lesson 3. If bigger discounts keep fooling you, read lesson 4. The integrated practice set mixes all four.
Every lesson has one original worked example, one likely mistake with its check, and one question to try yourself. Read the example slowly, cover the working, and try to reproduce it before moving on.
You can explore how the base changes with the percentage base and index explorer. For a teacher to go through your reasoning, see online one-to-one Mathematics tuition.