An expert question on clever sums for P5–P6, with a step-by-step solution, diagrams and the answer. The first few questions of a competition paper are often clever sums, and the Hua Xia Cup has them in every year from P1 to P6.
💡Hint 1: How is 5.12 related to 2.56? And 83.72 to 41.86?
💡Hint 2: Split a square's side into A and B: the big square = A × A + B × B + 2 × A × B. What square is in the brackets?
💡Hint 3: The first part is (2.56 + 34.44)² and the brackets hold (41.86 − 36.86)². Both bases are whole numbers.
Worked solution
Have a go first, then read the solution step by step.
1.Write the four numbers as fractions: A = 256/100, B = 3444/100, C = 4186/100, D = 3686/100. In the third term 512/100 = 2 × 256/100 = 2 × A; in the brackets 8372/100 = 2 × C.
2.The first part = A × A + B × B + 2 × A × B = (A + B) × (A + B) (a square of side A + B). A + B = (256 + 3444)/100 = 3700/100 = 37.
3.The brackets = C × C + D × D − 2 × C × D = (C − D) × (C − D) (a square of side C with two strips cut off). C − D = (4186 − 3686)/100 = 500/100 = 5.
⚠️Common mistake: applying the minus only to the first term in the brackets; every term inside changes sign. Others miss that 512/100 is twice A and grind out four multiplications.
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