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Topic Percentages & Estimation

Question

What is the "swap" trick, x% of y = y% of x, and why is it so useful?

Answer

You can flip which number is the percentage — because a%·b = (a·b)/100 = b%·a — turning a hard percentage into an easy one.

  • 8% of 25 looks awkward → swap to 25% of 8 = a quarter of 8 = 2.
  • 4% of 75 → 75% of 4 = 3.
  • 18% of 50 → 50% of 18 = 9.

Both sides are literally the same product over 100, so the answer is identical — you just pick the orientation your head finds easier (often one side becomes "a half / quarter / tenth of a small number").

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Topic Percentages & Estimation

Question

What is rounding estimation, and how do you keep the estimate honest?

Answer

Round each number to something easy, compute, and track whether you rounded up or down so you know which way the true answer leans.

  • 312 + 488 → 300 + 500 = ~800 (actual 800).
  • 47 × 19 → 47 × 20 = 940, but you rounded 19 up by 1 (≈ one 47 too many), so the true value is a bit under 940 (actual 893).

Rounding both numbers the same direction inflates or deflates the estimate predictably; rounding in opposite directions tends to cancel and gives a tighter estimate.

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