Read it again any time, including while you work through the exercises.
A price increases by 10%, then decreases by 10%. Does it come back to where it started? Almost everyone says yes... and it is wrong! This is one of the most famous traps in mathematics, and by the end of this lesson it will never catch you again.
The key is multiplier coefficients. Two successive changes combine by multiplying their coefficients. A 10% increase (coefficient 1.1) followed by a 10% decrease (coefficient 0.9) gives an overall coefficient of 1.1 × 0.9 = 0.99. The final price is 99% of the initial price: it went down by 1%.
Why? Because the 10% decrease applies to the new, higher price, not to the starting price. Successive percentages never add up: they multiply through their coefficients.
Another trap: getting back to the initial value. An item costs 60 € after a 20% discount: what was its price before? The wrong reflex is to add 20% of 60. The right reasoning: the 60 € price comes from a multiplication by 0.8, so to go back you divide by 0.8: the initial price was 60 ÷ 0.8 = 75 €. To undo a multiplication, you divide by the coefficient.
In this lesson you will combine changes, compute overall changes and travel back in time through prices. With coefficients in hand, no trap can hold.