basic proportions, why the results are inconsistent? Simple 3rd grade problem: A friend got a 10% raise to its salary. He got angry and asked for more. After much Negotiation he got another 10% raise on top of the first one. He asked me to check how better is he fairing with the 2 salary raises. I told him: you can either multiply like this > x * 1.1 * 1.1 = 1.21 * x which we know that he is going to get, overall, 21% of a raise and them I told him that he could check it by this simple division x = new salary in dollars / old salary in dollars. But he told me that he as getting 22% as a result. am I going crazy and not being able to do simple multiplication or he did the division wrongly?

He is doing it wrong.

If the start amount was 100$:

10% of 100\$ is 10\$, which after one raise gives you 110\$. 10% of this new amount is 11\$, which put on top gives 121\$.

What you get: $$100\$*1.1*1.1=100\$*1.21=121\$$$

What he should get:

$$x=\frac{\text{amount after}}{\text{amount before}}=\frac{121\$}{100\$}=1.21\,\,\,\,\,\text{ which is a raise of 21%}$$