Axiom

Fun Fact : How to Quickly Calculate Percentages
One trick that will often help you quickly calculate these types of percentages is to use the fact that x percent of y is the same as y percent of x. Huh? I know that might sound kind of confusing, but it’s actually pretty simple. Taking our example from before, this rule says that 36% of 25 is the same as 25% of 36. How does that help us? Well, since 25% is the same as the fraction 1/4, we see that 25% of 36 must be 36/4 or 9. So 25% of 36 is equal to 9, and 36% of 25 must also be 9.

It’s helpful to take a minute to see why this seemingly magical trick works. As I mentioned before, 36% is equivalent to the fraction 36/100. Since we can write the fraction 1/100 as the decimal number 0.01, we see that the fraction 36/100 can also be written 0.01 x 36. That means that 36% of 25 must be equal to (0.01 x 36) x 25. Now here comes the cool part: The associative property of multiplication tells us that we can multiply several numbers in any order we’d like. Which means that (0.01 x 36) x 25 = (0.01 x 25) x 36. But 0.01 x 25 is the same thing as 25%, which means that this is equal to 25% of 36. So 36% of 25 is equal to 25% of 36. It ain’t magic, it’s math! Pretty cool, right?