eli5 The percentage rule

Question

Can someone explain how/why X% of Y is equal to Y% of X? I know it’s true but I can’t figure out why. Thanks!

In: 10

Answer 1

I saw a lot of math, but I find it helpful to visualize it as objects instead of abstractions.

First, percentages are just factions. If we have 25%, that is the same as 25/100, 0.25, or 1/4. 100% is the same as 1.00. 3% is 0.03.

If I have 1 pies, and you get 1/4 (or 25%) of it, then you have 25% of that pie (1.00 x 25%). If you reverse it, then I have 1/4 of a pie, and you get 100% (or “1”) of what I have (¼ x 100%).

Or, if I have 4 kilograms of gold, and you get a 10% share of it, you get 0.4 kg (4.00 x 10%). If shares of gold are 0.1 each (0.1 = 10%), and you get 4 shares, you still get 0.4 kg (0.1 x 400%).

Hope this helps.

Answer 2

I saw a lot of math, but I find it helpful to visualize it as objects instead of abstractions.

First, percentages are just factions. If we have 25%, that is the same as 25/100, 0.25, or 1/4. 100% is the same as 1.00. 3% is 0.03.

If I have 1 pies, and you get 1/4 (or 25%) of it, then you have 25% of that pie (1.00 x 25%). If you reverse it, then I have 1/4 of a pie, and you get 100% (or “1”) of what I have (¼ x 100%).

Or, if I have 4 kilograms of gold, and you get a 10% share of it, you get 0.4 kg (4.00 x 10%). If shares of gold are 0.1 each (0.1 = 10%), and you get 4 shares, you still get 0.4 kg (0.1 x 400%).

Hope this helps.