Percent and percentage points
How "rose by 5 %" differs from "rose by 5 percentage points": a rate of 20 % to 25 %, the share of top pupils, a bank problem. This follows the Ukrainian Year 9 algebra book, the page "How to avoid ambiguity in percent problems".
- Germany: grade 6
- Ukraine: grade 9
Guide
In the Ukrainian Year 9 algebra book (after section 18) there is a page "How to avoid ambiguity in percent problems". An interest rate is a quantity like speed or price, except that it is itself expressed in percent. So "the rate rose by 10 %" can mean x + 10 (10 is added to the rate) or 1.1x (the rate rose by a tenth of itself).
To avoid this, economics uses percentage points. If an indicator of "20 %" rises to "25 %", it rose by 5 percentage points. But "the number of top pupils rose by 5 %" means 5 % of the number itself: from 20 people to 21.
The rule: percentage points are the difference of two percents; subtract one percent from the other. A percent change is a part of the quantity itself: multiply it by 1 + p100.
All the problems here use these words, like the bank problem of the book, restated. The "why" question asks you to explain the difference between the two ways of saying it.