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Percentages · level 2

Flip the percentage

x% of y always equals y% of x. When one side is awkward, swap them — 8% of 350 looks like work, 350% of 8 is 3.5 × 8 = 28 on sight.

Worked example: 8% of 350

asked8% of 350
flipped350% of 8
answer28

Step by step

  1. 1

    Percentages are reversible

    8% of 350 = 350% of 8

    Both are pct × n ÷ 100, so pick whichever way round is easier.

  2. 2

    Take the easy side

    350% of 8 = 3.5 × 8 = 28

8% of 350 = 28

The theory behind it

Intuition

Any percentage is built from 10% and 1% blocks: 17% = 10% + 5% + 2%. Because x% of y equals y% of x, you can always take the easier direction.

Common pitfalls

  • ×Adding percentage points to percentage changes — a rise from 4% to 6% margin is +2pp, not +2%.
  • ×Reversing a discount by adding the same percentage back: −20% then +20% does not return to par.

In the interview

Margin, growth, share and discount questions — the single most common arithmetic in an interview.