I was helping my sister learn percentages. We've got a simple exercise: product X costs $153.75$ including 23% tax. Calculate price without tax.
Now, the answer is of course to solve $1.23x = 153.75$. She however tried another way: $153.75 - 0.23 \cdot 153.75 = x$ with intuition to just subtract the tax from price. This is obviously wrong. I showed her the right way and we worked another example where the tax was 100% (and where the error is obvious).
She now knows that the second way is wrong, she sees the numbers that come out... but she told me that she still does not understand why exactly the second method does not work. And I couldn't find a way to explain this without using examples with specific numbers.
Question: How to explain this problem?