01 / MENTAL MATHS
Multiply by 11.
Keep the outside digits. Add them in the middle. Then discover what happens when you need to carry.
Try the exampleWATCH IT. TRY IT. UNDERSTAND IT.
Two discounts. One surprise.
20% off, then another 20%, gives 36% off overall. Change the offers and watch what happens to the price.
The example is loaded. Try a different number whenever you’re ready.
YOUR INTERACTIVE EXAMPLE
Make it yours.
A LITTLE PRACTICE. A REAL “I GET IT”.
Your turn.
Can you call it?
Make a prediction before you reveal the answer. Use the method you just explored.
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Challenge 1 of 5
THE BIT THAT MAKES IT CLICK
Why does it work?
The first discount leaves a fraction (1 − a/100) of the original price. The second applies to that reduced amount, leaving another fraction (1 − b/100). Multiply those fractions together. The combined percentage discount is a + b − ab/100, not simply a + b.
Where this experiment applies
Percentage reductions only: 0–100% each; price $0–$100,000. The model applies both factors before rounding the final amount to the nearest cent. A checkout that rounds at each stage can differ by a penny. Fees, tax changes and excluded items are outside this example.
THE RULE, IN ONE LINE
Keep (1 − a/100) × (1 − b/100)
The explanation and the answer use the same numbers.KEEP THAT CURIOSITY GOING
One more “aha”?
02 / PERCENTAGES
Flip the percentage.
If 8% of 50 feels awkward, try 50% of 8. Swap the numbers, keep the answer, and see why it works.
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