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PSLE Maths careless mistake

Adding and dividing fractions: the 2/5 mistake

The classic line on the script is 1/2 + 1/3 = 2/5. The same habit shows up when comparing (5/6 against 7/9 "because 7 is bigger") and when dividing (8 ÷ 2/3 worked as 8 × 2/3). Each is a rule applied where it does not belong.

What it looks like

PSLE-style question · 1 mark

Find the value of 1/2 + 1/3.

  1. Make the pieces the same size. The common denominator is 6: 1/2 = 3/6 and 1/3 = 2/6
  2. 3/6 + 2/6 = 5/6
2/5 5/6 ✓

Why 2/5 is wrong: Tops were added (1 + 1) and bottoms were added (2 + 3). Fractions can only be added when the pieces are the same size.

Why children do it

  • Multiplying fractions does work across the top and across the bottom, so the same move feels right for adding.
  • Fractions with different denominators are different-sized pieces, and that picture fades under exam pressure.
  • Dividing by a fraction needs the second fraction flipped; flipping the first, or none, gives a tidy wrong answer.

How to fix it at home

  • Fold a strip of paper into halves, then into thirds, and find where sixths come from. Ten minutes once is worth weeks of telling.
  • Before adding or subtracting, have your child write "same bottom?" and fix the denominators first.
  • For dividing, say the rule in full each time: keep the first, change ÷ to ×, flip the second.
  • Check with size: 1/2 + 1/3 must be more than 1/2, so 2/5 cannot be right.

Questions parents ask

Is dividing by a fraction in the PSLE?

Yes. Dividing a whole number or a proper fraction by a proper fraction is a P6 syllabus item and appears in Paper 1 most years.

Why does my child get multiplication right but not addition?

Multiplication is the one case where working straight across is correct, so it becomes the default move for every operation.

How does Knowbotic catch it?

Answers like 2/5 are known traps on fraction questions, so the wrong answer is named as this habit and practised until it is right three times in a row.

Where it shows up

Fractions

Other careless mistakes

Fraction of a remainderMinutes and hours (60, not 100)Percentage of a new totalFound the increase, not the new priceStopped at one part in ratioSimplest form in final fraction answersLeft out the unitsConverting units (kg, ℓ, m, cm³)Collecting like terms in algebraAngle facts (straight line, triangle, quadrilateral)Area, perimeter and volume formulasRadius and diameter in circlesAverage and totalFactors and multiples (HCF, LCM)Calculation slipPlace value and roundingOrder of operationsDecimals: the point and the placesAlgebra: forming, substituting and solvingNumber patterns: the rule and the termReading graphs, tables and scalesNets and solids: faces, edges and verticesAnswered the part not asked for

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