Did you know? Reversing a percentage comparison usually changes the answer because it changes the reference quantity. Help a Secondary 3 student identify what counts as 100%, calculate the difference and divide by the named base. The same numerical gap can represent different percentages.
Try these original quantities: A is 80 and B is 100. B is 25% greater than A because 20 ÷ 80 × 100 = 25%. A is 20% less than B because 20 ÷ 100 × 100 = 20%. The difference stays 20, but the reference changes.
Use the Mathematics taught at the student’s actual G level and current topic. PG1–3 are admission Posting Groups, not a complete subject-level description. This workshop focuses on reversed comparisons, not every percentage problem or an identical G1/G2/G3 syllabus checklist.
eduKateSengkang · Secondary 3 learning
Find your next learning step
Choose the question closest to today’s difficulty. Each section offers a small action and a way to check understanding.
1. Turn the wording into a reference statement
2. Find the difference separately
3. Calculate both directions explicitly
4. Connect carefully to increase and decrease
5. Retest with a different pair
Open all six learning steps · Subject-by-subject learning plan
Contents: six practical learning steps
In “B is greater than A”, the percentage comparison uses A as its reference. Write “A = 100% of the comparison base” before calculating. In the reversed question, B becomes the reference.
Ask the learner to complete “compared with …”. This small language check can reveal a misunderstanding before arithmetic starts. Do not choose the larger quantity as the denominator simply because it looks like the whole.
Our difference is 100 − 80 = 20. This is an amount, not yet a percentage. Keep it separate from the reference so the student can explain what each part of the calculation represents.
A correct subtraction does not prove the denominator is correct. Percentage errors often arise after the difference has been found accurately. Check meaning at the division step rather than assigning more subtraction practice automatically.
For B compared with A, divide 20 by 80 to obtain 25%. For A compared with B, divide 20 by 100 to obtain 20%. Label both results with the direction they describe.
Do not report only “the percentage difference is 25%” when the task’s reference matters. The reader needs to know which quantity is being compared with which. Follow the wording rather than treating the two directions as interchangeable.
Twenty-five per cent of 80 is 20; adding it gives 100. Twenty per cent of 100 is 20; subtracting it gives 80. Both results return to the original quantities when used with the correct base.
If a learner claims A is 25% less than B, check 25% of 100. It gives 25, leaving 75 rather than 80. The reverse calculation exposes the reference mismatch without needing a new formula.
If one quantity changes from 80 to 100, the increase is 25% of its starting value. A change from 100 back to 80 is a 20% decrease from that new starting value. Equal opposite amounts are not necessarily equal opposite percentages.
Our first example compares two quantities, while this example describes a sequence in time. Keep those meanings distinct. Do not invent a before-and-after story when the question only supplies a comparison.
Try A = 60 and B = 90. B is 50% greater than A because 30 ÷ 60 = 0.5. A is one-third less than B, or 33⅓%, because 30 ÷ 90 = one-third.
Ask for the base before the calculation and a reverse check afterwards. Track wording, reference and arithmetic separately. The wider Maths guide develops the learning route; later SEC revision requires the correct subject syllabus and examination year.
Useful learning routes
Connect with the after-PSLE foundations · Find your subject-specific SEC route
Official sources and scope
MOE G2 and G3 Mathematics syllabuses
SEAB SEC school-candidate syllabus directory
Practice situations and routines in this guide are original teaching illustrations, not official examination questions or marking schemes. Official sources provide curriculum context; follow current school instructions and the applicable subject-level syllabus.
