PSLE Mathematics Learning Guide · Guide 21
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Percentage problems often go wrong because the learner remembers the percentage but loses the quantity it belongs to. A 20% increase is 20% of the original quantity. A 20% discount is 20% of the original marked price. A second percentage applied after a change may use a new base.
This guide develops one habit: name the base, convert the change into a percentage state, calculate the change or final value, then check whether every later percentage still refers to the same base.
The MOE Primary Mathematics syllabus updated October 2025 provides the current curriculum context, and the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples below are original eduKate teaching material.
A percentage always has a base
20% of $50 is $10. Twenty percent of $80 is $16. The percentage is identical; the base is not.
Before calculating, complete the sentence:
“This percentage is of ______.”
If the blank cannot be filled with a specific quantity, calculation should wait.
Increase by a percentage
A quantity of 120 increases by 25%.
Increase = 25% of 120 = 30.
Final value = 120 + 30 = 150.
Equivalent percentage-state method:
100% + 25% = 125%.
125% of 120 = 150.
Decrease by a percentage
A quantity of 200 decreases by 15%.
Decrease = 15% of 200 = 30.
Final value = 170.
Or final = 85% of original = 0.85 × 200 = 170.
Discount is a percentage decrease from the marked price
A bag is marked at $80 and discounted by 25%.
Discount = 25% of $80 = $20.
Sale price = $60.
Equivalent method: sale price = 75% of $80 = $60.
The base is the original marked price unless the problem states otherwise.
Reverse percentage starts from the final percentage state
A jacket costs $72 after a 20% discount. What was the marked price?
After a 20% discount, the sale price is 80% of the marked price.
So 80% = $72.
100% = 72 ÷ 0.8 = $90.
Subtracting 20% of $72 would be wrong because the 20% discount was not defined from the final price.
Successive percentage changes may use different bases
A price of $100 is reduced by 20%, then the reduced price is increased by 20%.
After decrease: $80.
Increase = 20% of $80 = $16.
Final price = $96.
The two 20% changes do not cancel because they use different bases.
Do not confuse percentage change with percentage-point change
Suppose a class success rate changes from 60% to 75%.
The increase is 15 percentage points.
Relative percentage increase = 15/60 × 100% = 25%.
These are different descriptions. In primary tasks, follow the wording carefully and do not substitute one for the other.
Fractions, decimals and percentages can cross-check one another
25% = 1/4 = 0.25.
75% = 3/4 = 0.75.
12.5% = 1/8 = 0.125.
Converting to a familiar fraction can make mental checking easier.
Main worked workshop: sixteen original percentage problems
1.
Increase 80 by 25%.
Answer: 100.
2.
Decrease 240 by 10%.
Answer: 216.
3.
A $50 item has 30% discount.
Answer: $35.
4.
A $120 item has 15% discount.
Answer: $102.
5.
A quantity becomes 132 after a 10% increase. Find original.
Answer: 132 ÷ 1.1 = 120.
6.
A price becomes $63 after a 30% discount. Find marked price.
Answer: 63 ÷ 0.7 = $90.
7.
200 is increased by 20% then decreased by 20%.
Answer: 200→240→192.
8.
200 is decreased by 20% then increased by 20%.
Answer: 200→160→192.
9.
A school club grows from 80 to 100 members. Find percentage increase.
Reasoning: Increase 20; 20/80 ×100%=25%.
10.
A collection falls from 150 to 120. Find percentage decrease.
Reasoning: Decrease 30; 30/150 ×100%=20%.
11.
40% of a number is 36. Find number.
Answer: 36 ÷ 0.4 = 90.
12.
A price is 125% of its original value and equals $250.
Answer: $200.
13.
25% of the remaining $80 is spent. How much?
Answer: $20.
14.
A learner adds 20% and 30% in two successive changes and says total change is always 50%.
Repair: Only valid if both percentages share the same base in an additive relationship. Successive changes often use new bases.
15.
A $90 item is discounted 20%, then another 10% off the sale price.
Answer: 90×0.8×0.9=$64.80.
16.
A number increases from 60 to 75. State both percentage-point and relative percentage changes if interpreted as a percentage rate.
Answer: 15 percentage points; 25% relative increase.
A percentage-state table
| Change | Final as % of original |
|---|---|
| increase 10% | 110% |
| increase 25% | 125% |
| decrease 10% | 90% |
| discount 30% | 70% |
| discount 45% | 55% |
Common percentage errors
Error 1: Use the final value as the base for an original-value percentage.
Error 2: Add successive percentage changes that use different bases.
Error 3: Subtract the percentage number instead of the percentage amount.
Error 4: Treat “20% more than” as “120 more”.
Error 5: Reverse a discount by adding the same percentage to the sale price.
Independent transfer check
- Increase 160 by 15%.
- Decrease 500 by 12%.
- A $240 item has a 25% discount. Find sale price.
- A sale price is $84 after a 30% discount. Find marked price.
- A population rises from 200 to 250. Find percentage increase.
- A value falls from 400 to 340. Find percentage decrease.
- Explain why a 20% decrease followed by a 20% increase does not restore the original value.
- Explain what base a discount percentage normally uses.
Independent-check answers
1. 184.
2. 440.
3. $180.
4. $120.
5. 25%.
6. 15%.
7. The increase is calculated from the smaller post-decrease base.
8. The original marked price unless the problem states a different reference.
Parent and tutor guide
Ask “percentage of what?” before allowing any percentage multiplication. For reverse percentage, write the final percentage state first: “sale price = 70% of marked price”.
If successive changes are confused, draw a short state chain with the amount after each step. Do not compress the percentages until the base relationship is clear.
The learner’s final card
Percentage of what? Is this the original, remaining or final value? What percentage of the original does the final state represent? Do later percentages use the same base?
Continue through the PSLE Mathematics Learning Guide
Continue with Guide 22: Number Patterns, Guide 23: Symmetry, and Guide 24: Coordinates and Grid Position.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and suggested solutions are original eduKate teaching material. Percentage-point terminology is included only to clarify a common language distinction, not as an assertion that every such task is assessed at PSLE.