# Computing Percentages Easier

Solution: 16% of 25 is equivalent to 25% of 16, which is clearly 4. This is true for all numbers: $x\%$ of $y$ is always equal to $y\%$ of $x$. The first one is $\frac{x}{100} y$ and the second is $\frac{y}{100}x$, and because multiplication is commutative and associative, both are equal to $(x \cdot y) / 100$. You can pick the version that is easiest.
Viewing the mental arithmetic as a math puzzle inspires all kinds of creativity. You can compute “$x\%$ of $y$” in their head by first computing 1% of $y$ and then scaling it up by $x$. Or you can split the denominator 100 into two pieces, such as $((x / 10) \cdot (y / 10))$, which is the same as “compute 10% of x and y separately, then multiply them together,” making a problem like 40% of 70 = 28 seem less intimidating than the “multiply then divide by 100” approach. The common 20% gratuity calculation is “move the decimal place over by 1 and double it,” i.e., $\frac{x}{100} \cdot 20 = \frac{2 \cdot 10 \cdot x}{10 \cdot 10} = \frac{2 \cdot x}{10}$.