Level 5 · Ages 15–16
Read it again any time, including while you work through the exercises.
A price goes up by 15%. You could compute the 15%, then add it to the price. But there is a powerful shortcut: the multiplier coefficient. Increasing by 15% means multiplying by 1.15. One operation instead of two.
Where does this 1.15 come from? The starting price is 100% of itself. After a 15% increase, the new price is 100% + 15% = 115% of the old one, that is 115/100 = 1.15 times the old one. Increasing by t% means multiplying by 1 + t/100.
For a decrease, same logic in reverse. Dropping by 20% means keeping 100% - 20% = 80% of the price: you multiply by 0.80. Decreasing by t% means multiplying by 1 - t/100. Keep the reflex: an increase gives a coefficient greater than 1, a decrease gives a coefficient smaller than 1.
This shortcut also works backwards: if you know the coefficient, you can read the change. Multiplying by 0.85 means decreasing by 15%. And to find a percentage change between two values, divide the variation by the starting value: going from 50 to 62 is a variation of 12, and 12/50 = 24/100, a 24% increase.
This lesson gives you the central tool for all percentage changes: you will turn percentages into coefficients and coefficients into percentages, in both directions.
A subscription costs 60 €. Its price increases by 15%. What is the new price?
1 + 15/100 = 1.15
I turn the increase into a coefficient: increasing by 15% means multiplying by 1.15.
60 × 1.15 = 69
I apply the coefficient to the starting price: 60 × 1.15 = 69.
60 + 9 = 69
I check another way: 15% of 60 = 9, and 60 + 9 = 69. Both methods agree.
Result: The new price is 69 €.
A pair of jeans costs 45 €. Its price drops by 20%. What is the new price?
1 - 20/100 = 0.80
Dropping by 20% means keeping 80% of the price: I multiply by 0.80.
45 × 0.80 = 36
I apply the coefficient: 45 × 0.8 = 36.
Result: The new price is 36 €.