Did you know? If a price increases by 20% and later decreases by 20%, it does not return to its original amount. The percentages are applied to different starting values. This is one of the most useful lessons in Secondary 4 G1 Mathematics: always know which quantity represents 100%.
Quick answer for Bukit Timah parents: the 2027 SEC G1 Mathematics K110 syllabus includes finding the whole from a percentage part, percentages greater than 100%, comparing quantities by percentage, and percentage increases and decreases. A tutor should check whether a student recognises the base before calculating.
Every percentage needs a reference quantity
A percentage is a ratio out of one hundred. Saying “35 is 70%” leaves an important question: 70% of what? If 35 is 70% of a whole, the whole is 35 ÷ 0.70 = 50.
This is a reverse-percentage problem. Multiplying 35 by 0.70 would make the number even smaller and answer a different question. Draw a bar divided into ten equal parts: seven parts represent 35, so each part represents five. All ten parts represent 50.
Worked example 1: recovering an original price
An illustrative item is sold for $90 after a 25% discount. What was its original price? A 25% discount leaves 75% of the original. So 0.75 × original price = 90, and the original price is $90 ÷ 0.75 = $120.
Check: 25% of $120 is $30. Subtract $30 from $120 and you get $90. The verification uses the original price, not the discounted price.
Worked example 2: percentages can exceed 100%
Suppose an after-school club has 40 members this year and 54 next year. Next year’s membership is 54/40 × 100% = 135% of this year’s figure. That is mathematically sensible: 100% would mean no numerical change, while 135% means a larger amount.
The percentage increase, however, is (54 − 40)/40 × 100% = 35%. Be careful: “135% of the original” and “an increase of 135%” do not mean the same thing. The latter would result in 235% of the starting amount.
If a question asks for 150% of 60, the calculation is 1.5 × 60 = 90. A student who assumes every percentage must be at most 100% may hesitate unnecessarily.
Worked example 3: equal percentage increases and decreases
A hypothetical price begins at $100. After a 20% increase, it becomes $100 × 1.20 = $120. A later 20% reduction is then applied to $120, so the new price is $120 × 0.80 = $96.
The final amount is $4 below the original, a 4% overall decrease. You cannot simply cancel the +20% and −20% because the two percentages use different bases. The mathematical multiplier is 1.20 × 0.80 = 0.96.
This is a made-up arithmetic example, not a prediction about retail prices in Bukit Timah. The principle also applies to some percentage comparisons in populations, quantities and measured values.
Worked example 4: percentage change is measured from the starting value
A number increases from 80 to 124. The difference is 124 − 80 = 44. Percentage increase = 44/80 × 100% = 55%.
Suppose it then returns from 124 to 80. Percentage decrease is 44/124 × 100% ≈ 35.5%, not 55%. The amount of change is the same 44, but the starting base is now 124. For exam questions, give the requested accuracy and show the denominator selected.
The quick base-first method
- Underline the base: decide which amount represents the original 100%.
- Name the question type: are you finding a part, a whole, a percentage of another value, or a percentage change?
- Convert carefully: 70% becomes 0.70, 135% becomes 1.35, and 25% off leaves 0.75.
- Write the equation: for example, 0.75 × original = sale price.
- Check the direction: the original price before a reduction should be larger than the reduced price.
What is examinable in K110?
The published 2027 SEAB K110 Mathematics syllabus includes expressing percentages as fractions or decimals, finding the whole given a percentage part, percentages greater than 100%, comparing values by percentage, and increasing or decreasing quantities by a specified percentage. These are listed under N3, Percentage, within Number and Algebra.
Number and Algebra appears in both SEC K110 Mathematics papers. Questions may also place percentage skills into real-world contexts such as household finance, but the four examples here are original classroom examples rather than actual examination items.
The SEAB 2027 G1 subject list identifies K110 as the 2027 Mathematics code and shows 4046 for 2026 and earlier reference. For a student sitting examinations in 2026, follow that student’s registered exam syllabus rather than assuming that 2027 coding applies.
A five-minute parent check
Try three questions: (1) 24 is 60% of what? Answer: 40. (2) 125% of 80 equals what? Answer: 100. (3) A price decreases from $50 to $40. What is the percentage decrease? Answer: 20%. After each answer, ask the student to explain which number was treated as 100%.
A tutor who listens to that explanation can tell whether a wrong answer came from the base amount, decimal conversion or arithmetic. The unchanged eduKateSG three-pupil Clementi Mathematics tutorial reference shows an individual-feedback approach for a different Secondary 1 offering; confirm current Secondary 4 G1 class availability and location directly.
Frequently asked questions
Can a percentage exceed 100%? Yes. An amount can be 125% or 200% of a reference amount; that means it is larger than the reference.
Is ‘25% off’ the same as ‘divide by 1.25’? No. A 25% discount leaves 75%, while a 25% mark-up produces 125%. The reverse operation depends on what happened.
How can I recognise a reverse-percentage problem? Usually a part or changed amount is given and the question asks for the original whole.
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