Whenever you use portions, be clear about what is the whole from which these portions come. They’re not just portions, per se. They’re portions of something.

For example, let’s say we have 16 pencils and we wish to get rid of a fourth (or a quarter) of them. One fourth of 16 is 4. So we get rid of 4 pencils. Now we only have 12 pencils.

Here comes Eliana. Hi, Eliana!

We ask Eliana to add a fourth (or a quarter). She sees 12 pencils. She correctly calculates that a fourth of 12 is 3. So she adds 3 pencils. Now we have 15 pencils!

Maybe you can now see what’s happening here.

When we subtracted a fourth, we could have asked: “A fourth of what?” And the answer would have been: “A fourth of 16.” This means that, for us, 16 is the whole from which we were taking a fourth.

When Eliana added a fourth, we could have asked: “A fourth of what?” And Eliana would have answered: “A fourth of 12.” This means that, for Eliana, 12 is the whole to which we are adding a fourth.

A fourth of 16 is not the same as a fourth of 12.

Percentages are portions. And the same rule applies.

We can present the same example as percentages.

From our 100% of 16 pencils, we got rid of 25% of them, so we were left with 75% of what we had, that is: 12 pencils.

Then Eliana added 25% to that. 25% of 12 is 3. So now we have 15 pencils.

We didn’t end up with 16 pencils because 25% of 16 is not the same as 25% of 12.