Primary 6 Maths: Percentage
PSLE percentage goes past P5's basics: percentage change, reverse percentage (finding the whole), discount and GST, and percentage of a percentage — worked examples aligned to the MOE syllabus.
Most schools typically cover this topic in Term 1, around weeks 5–7 — though every school sets its own sequence.
By Primary 6, percentage stops being "find the part" and turns into "work out what changed, or work backwards to what you started with." P5 Percentage builds the conversions and the forward direction — given the whole, find the part or the percentage. P6 percentage builds on that base with the questions PSLE actually leans on: percentage increase and decrease, reverse percentage (given the changed amount, find the original), discount combined with GST, and percentage of a percentage layered two or three deep.
The single most useful habit at this level is naming what 100% stands for before calculating anything. A discounted price is not 100% of the original — it's less than 100%, and every reverse-percentage mistake traces back to skipping that step.
The mistakes to watch for
- Treating the discounted or increased amount as 100%. After a 20% discount, the price paid is 80% of the original — not 100%, and not the number to build the ratio from.
- Adding and subtracting percentages that describe different wholes. A 20% increase followed by a 25% decrease is not a net 5% decrease, because the 25% is taken off a larger new amount, not the original. Multiply the scale factors instead: 1.20 × 0.75 = 0.90, a net 10% decrease.
- Applying GST before the discount, or to the original price instead of the discounted price. GST in Singapore is charged on the price actually paid — after any discount — not on the original ticket price. (GST is 9% since 1 January 2024.)
- Losing track of the base in a percentage-of-a-percentage question. "20% of the pupils in CCA A are in the choir" is 20% of CCA A's pupils, not 20% of the whole school — convert each layer to a percentage of the same whole before combining.
Percentage change and reverse percentage
Easy: percentage change, discount and GST warm-ups
Easy: percentage increase
A shop increased the price of a toy from $40 to $50. Find the percentage increase.
Show the worked solution
Increase = $50 − $40 = $10.
Percentage increase = 10/40 × 100% = 25%.
Easy: percentage decrease
A town's population decreased from 5000 to 4600. Find the percentage decrease.
Show the worked solution
Decrease = 5000 − 4600 = 400.
Percentage decrease = 400/5000 × 100% = 8%.
Easy: a simple discount
A bag originally costs $80. It is on sale at a 15% discount. Find the sale price.
Show the worked solution
Discount amount = 15% of $80 = 15/100 × 80 = $12.
Sale price = $80 − $12 = $68.
Easy: adding GST
A meal costs $50 before GST. GST is 9%. Find the total price including GST.
Show the worked solution
GST amount = 9% of $50 = 9/100 × 50 = $4.50.
Total price = $50 + $4.50 = $54.50.
Exam: reverse percentage and layered percentages
Exam: reverse percentage from a discount
After a 20% discount, a jacket costs $96. Find the original price.
Show the worked solution
The $96 paid is 100% − 20% = 80% of the original price.
80% of the price = $96, so 20% (a quarter of 80%) = $24.
Original price = 100% = 5 × $24 = $120.
Check: 20% of $120 = $24 off → $96 paid. ✓
Exam: reverse percentage from an increase
A company's profit increased by 15% to reach $46,000 this year. Find last year's profit.
Show the worked solution
This year's profit is 100% + 15% = 115% of last year's profit.
115% of last year's profit = $46,000, so 1% = $400.
Last year's profit = 100% = 100 × $400 = $40,000.
Check: $40,000 × 1.15 = $46,000. ✓
Exam: discount, then GST
A laptop is priced at $1200. It is on sale at a 10% discount, and 9% GST is then charged on the discounted price. Find the final price the customer pays.
Show the worked solution
Discounted price = 90% of $1200 = 1200 × 0.9 = $1080.
GST is charged on the $1080 actually being paid, not on the original $1200: GST = 9% of $1080 = $97.20.
Final price = $1080 + $97.20 = $1177.20.
Exam: percentage of a percentage
In a school, 45% of the pupils take part in CCA A. 20% of the pupils in CCA A are in the choir. If 27 pupils are in the choir, how many pupils are there in the school in total?
Show the worked solution
The choir is 20% of CCA A, and CCA A is 45% of the school, so the choir is 20% of 45% of the whole school.
20% of 45% = 0.20 × 0.45 = 0.09 = 9% of the school.
9% of the school = 27 pupils, so 1% = 3 pupils.
Total pupils = 100 × 3 = 300 pupils.
Check: 45% of 300 = 135 pupils in CCA A; 20% of 135 = 27 in the choir. ✓
Exam: percentage combined with a fraction
1/4 of a bookshop's books are fiction. The rest are non-fiction. 20% of the non-fiction books are biographies. What percentage of all the books in the shop are biographies?
Show the worked solution
Fiction = 1/4 = 25% of all books, so non-fiction = 100% − 25% = 75%.
Biographies = 20% of the non-fiction books = 20% of 75% = 0.20 × 0.75 = 0.15 = 15% of all the books.
PSLE challenge: multi-step PSLE percentage problems
PSLE challenge: percentage combined with ratio
Ali and Ben shared a sum of money in the ratio 3 : 5. Ali then donated 20% of his share to charity, and his donation came to $18. How much money did Ali and Ben share altogether?
Show the worked solution
Let 1 unit of the ratio = u. Ali's share = 3u.
Ali's donation = 20% of his share: 0.20 × 3u = 0.6u = $18, so u = $30.
Total shared = 3u + 5u = 8u = 8 × $30 = $240.
Check: Ali's share = 3 × $30 = $90; 20% of $90 = $18. ✓
PSLE challenge: two successive percentage changes
The price of a phone was increased by 20%, and later decreased by 25% in a sale. The final price is $540. Find the original price.
Show the worked solution
The two changes are not "20% − 25% = −5% net" — each percentage applies to a different amount. Multiply the scale factors instead.
Final price = original × 1.20 × 0.75 = original × 0.90.
original × 0.90 = $540, so original = 540 ÷ 0.9 = $600.
Check: $600 × 1.20 = $720; $720 × 0.75 = $540. ✓
PSLE challenge: reverse percentage with discount and GST
Mrs Lee paid $872 for a washing machine after a 20% discount was applied, and 9% GST was then added to the discounted price. Find the original price of the washing machine before the discount.
Show the worked solution
Work backwards through the GST step first: the $872 paid is 100% + 9% = 109% of the discounted price.
Discounted price = 872 ÷ 1.09 = $800.
The $800 discounted price is 100% − 20% = 80% of the original price.
Original price = 800 ÷ 0.8 = $1000.
Check: $1000 × 0.8 = $800 discounted; $800 × 1.09 = $872 paid. ✓
How to practise this topic
Every question above resolves to naming 100% correctly and multiplying by a scale factor, so drill that step in isolation before drilling whole questions: given a scenario, write down what 100% represents first. PSLE percentage rarely appears alone — it's usually stacked with ratio or a fraction inside one multi-step question, so once the mechanics are solid, cross-train with P6 Ratio, P6 Fractions and PSLE problem-solving.
Source: MOE 2021 Primary Mathematics Syllabus (P1 to P6).
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 6 Percentage includes the concepts below. (P6-M-04 is Test Paper's own topic code, not an MOE reference.)
- Percentage of a quantity
- Percentage increase and decrease
- Discount and GST
- Percentage word problems
- Interconversion of fractions, decimals, and percentages
Before this topic
These topics feed into Percentage — if this one wobbles, check them first: Primary 5 Percentage · Primary 6 Fractions · Primary 6 Decimals.
Where to go next
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