Percentage
Learn how percentages work in everyday situations such as discounts, GST, service charge, profit and loss, commission, percentage change and reverse percentage.
This page helps Sec 1 students connect percentage formulae to real-world questions, so they do not just memorise steps without understanding the base quantity.
What students should be able to do
Percentage means parts out of 100
A percentage expresses a quantity as a number of parts out of 100. The symbol % means “per cent” or “per hundred”.
| Concept | Useful form | What to remember |
|---|---|---|
| Percentage as fraction and decimal | 𝑥% = 𝑥 / 100 | Example: 72% = 72/100 = 0.72. |
| Convert decimal to percentage | decimal × 100% | Example: 0.35 = 35%. |
| Percentage of a quantity | 𝑥% of a quantity = (𝑥/100) × quantity | The word “of” usually means multiply. |
| One quantity as percentage of another | (part / whole) × 100% | Both quantities must use the same unit. |
Find the part from the whole
To find a percentage of a quantity, convert the percentage to a fraction or decimal, then multiply by the quantity.
Identify the whole
Check what represents 100%.
Convert percentage
25% = 25/100 = 0.25.
Multiply
25% of 40 = 0.25 × 40 = 10.
60% of a class
Question: There are 25 girls in a class. 60% of the girls have long hair. How many girls have long hair?
60% of 25 = 60/100 × 25
= 0.6 × 25
= 15
Answer: 15 girls.
Use the correct base quantity
When comparing two quantities, the wording tells us which quantity is the base. The base quantity is the denominator.
Part as percentage of whole
There are 40 male teachers out of 90 teachers.
Male teachers as a percentage:
40/90 × 100% = 44.4% to 3 significant figures.
Quantity A compared with Quantity B
If A is 80% of B, then the base is B.
Common trap: “A is 80% of B” is not the same as “B is 80% of A”.
Important: Always check the wording “of”. It usually points to the base quantity.
Percentage increase or decrease uses the original value
Percentage change compares the amount of change with the original value. The original value is the base.
| Type | Formula idea | Example |
|---|---|---|
| Percentage increase | increase / original value × 100% | $1600 to $1680: increase = $80, so 80/1600 × 100% = 5%. |
| Percentage decrease | decrease / original value × 100% | $1600 to $1520: decrease = $80, so 80/1600 × 100% = 5%. |
| New value after change | new value = percentage of original value | Increase by 10% means new value is 110% of the original. |
Find the original 100%
In reverse percentage questions, the final value is given and students need to find the original value. The key question is: “What percentage does the final value represent?”
Example: After a 5% increase, a salary becomes $2205. Find the original salary.
After 5% increase, new salary = 105% of original.
105% represents $2205.
1% represents $2205 ÷ 105 = $21.
100% represents $21 × 100 = $2100.
Original salary: $2100.
Percentage point is not the same as percent change
If a rate increases from 5% to 7%, the increase is 2 percentage points. It is not simply a 2% increase.
Trap: From 5% to 7% is an increase of 2 percentage points, but the relative percent increase is 2/5 × 100% = 40%.
Use percentages in money and daily-life questions
Percentages appear in real-world contexts such as profit and loss, discounts, GST, service charge and commission. Students should always identify the base value before calculating.
Profit and loss
Profit = selling price − cost price.
Loss = cost price − selling price.
Discount
Discount = marked price − sale price.
Percentage discount uses marked price as the base.
GST and service charge
GST is currently 9% in Singapore. Apply it to the correct subtotal.
Commission
Commission is payment for selling or buying on behalf of another party.
Percentage greater than 100%
120% means more than the whole. It is 1.2 times the original.
Percentage less than 1%
0.5% means 0.5 out of 100, which is 0.005 as a decimal.
Watch for these mistakes
Using the wrong base
Percentage change uses the original value, not the final value.
Confusing percentage point and percent change
From 5% to 7% is 2 percentage points, not a 2% increase.
Averaging percentages blindly
Do not add or average percentages when the bases are different.
Reading discount / GST order wrongly
Check whether GST or service charge is applied before or after a discount.
Check readiness before doing the full worksheet
Try these 6 questions first. After clicking Check answers, each question will show a short explanation or trap reminder.
1. What is 35% as a decimal?
2. Find 20% of 150.
3. A price increases from $80 to $100. What is the percentage increase?
4. A discount reduces a $50 item to $40. What is the percentage discount?
5. A salary after a 10% increase is $2200. What was the original salary?
6. A rate changes from 5% to 7%. What is the change in percentage points?
Core examples to discuss in class
Example 1. Express 0.28 as a percentage.
Reveal working
0.28 × 100% = 28%.
Example 2. A bag costs $28 and is sold for $35. Find the profit as a percentage of the cost price.
Reveal working
Profit = $35 − $28 = $7.
Profit percentage = 7/28 × 100% = 25%.
Example 3. A meal costs $100 before service charge and GST. A 10% service charge is added, then 9% GST is charged on the subtotal. Find the final amount.
Reveal working
Service charge = 10% of $100 = $10.
Subtotal = $110.
GST = 9% of $110 = $9.90.
Final amount = $119.90.
Try a few questions before the PDF
These questions are for quick diagnosis. The full worksheet is in the PDF.
1. Express 48% as a decimal.
Reveal answer
48% = 0.48.
2. Find 15% of $240.
Reveal answer
15/100 × 240 = $36.
3. A value decreases from 500 to 450. Find the percentage decrease.
Reveal answer
Decrease = 50. Percentage decrease = 50/500 × 100% = 10%.
4. A sale price after a 20% discount is $64. Find the original marked price.
Reveal answer
After 20% discount, $64 is 80% of the original. Original = 64 ÷ 0.8 = $80.
Use the PDF for the full practice workload
The webpage teaches and diagnoses. The PDF carries the main practice work: conversions, percentage of a quantity, comparison, percentage change, reverse percentage, profit and loss, discount, GST and commission.
84 questions
Designed for sustained percentage practice across the chapter.
Worked examples
Includes reminders and examples before the practice sections.
Answers included
Includes answers, short explanations and teacher notes.
Suggested lesson flow
Ready to practise Percentage?
Download the printable worksheet, identify the base quantity carefully, and check whether the question is asking for the part, the whole, or the percentage.
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