To choose a method, ask three questions before you calculate: what do I know, what do I want, and what is the starting amount the percentage or ratio refers to. Write the answers down. They point to the method before any arithmetic begins.
Following an example feels like understanding, and it is a good first step. Choosing is the next skill, and it is learned by practising the decision itself.
Why is choosing harder than following?
In a worked example, the method is already chosen for you. You only carry it out. In an exam question, the choice is hidden inside the wording, and two questions that look alike can need opposite methods.
This is not a sign that you are weak. It is a sign that your practice has focused on calculating, and choosing needs its own practice.
How do I choose, step by step?
- Underline what you are given and circle what you must find.
- Name the type of problem in a few words: “percentage change”, “ratio share”, “rearranging”.
- Identify the reference amount: what is the percentage or ratio of?
- Predict the size of the answer: should it be bigger or smaller than the number given?
- Choose the method, then calculate.
- Check with your prediction and by substituting back.
Worked example
Compare two questions that look almost the same.
Question A: A price rises by 20% to reach RM60. What was the original price?
Question B: A price of RM60 rises by 20%. What is the new price?
Apply the steps to A.
- Given: new price RM60 after a 20% rise. Wanted: the original.
- The 20% refers to the original price, which is unknown.
- Prediction: the original must be smaller than 60.
The new price is 120% of the original, so original × 1.2 = 60, which gives 60 ÷ 1.2 = RM50. Check: 50 × 1.2 = 60 ✓.
Apply the steps to B.
- Given: original price RM60. Wanted: new price.
- The 20% refers to 60, which is known.
- Prediction: bigger than 60.
So 60 × 1.2 = RM72. Check: 20% of 60 is 12, and 60 + 12 = 72 ✓.
Same numbers, opposite methods. The difference was spotted by asking “what does the percentage refer to, and do I know that amount?”
What is a common mistake?
The common mistake is to pick the method from the numbers on the page, not from the situation. Seeing 60 and 20% leads straight to 60 × 1.2.
Mistaken answer to A: 60 × 1.2 = 72, so the original price was RM72.
The prediction step catches it: the original price must be less than 60, because the price rose.
The correction is to do the prediction before the calculation. Two seconds of “bigger or smaller?” removes a large share of method errors.
Check yourself
For each question, write the reference amount, your prediction and the answer.
1. After a 10% discount, a bag costs RM90. What was the price before the discount?
Show answer
The discount refers to the original price, which is unknown. The original is bigger than 90. The sale price is 90% of the original, so 90 ÷ 0.9 = RM100. Check: 100 × 0.9 = 90.
2. A bag costs RM90. It is discounted by 10%. What is the sale price?
Show answer
The reference amount is 90, which is known. The sale price is smaller than 90. 90 × 0.9 = RM81. Check: 10% of 90 is 9, and 90 − 9 = 81.
3. After a 25% increase, a rent is RM150. What was the rent before?
Show answer
The original is smaller than 150. 150 ÷ 1.25 = RM120. Check: 120 × 1.25 = 150.
What should I do next?
Practise with a mix, not a single topic. The original mixed-practice builder builds a short session of questions that do not label their method, so you have to choose. After each session, write one line on how you chose.
Read using a mistake log to spot a repeated pattern to track method-choice errors, and retesting a skill without repeating the same numbers to check that the skill has transferred. The students’ guide lists other situations.
If you still stall on unfamiliar questions after practising this way, the gap may be in a step you cannot see from the inside. A teacher in online one-to-one Mathematics tuition can give you new questions in the trial hour and ask you to explain your choice aloud.