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

25% of 80 is just 0.25×80=20

80% of 25 is just 25×0.8=20

All you’re doing is multiplying one of the numbers by 100 and dividing the other one by 100 when you switch X and Y

Answer 2

25% of 80 is just 0.25×80=20

80% of 25 is just 25×0.8=20

All you’re doing is multiplying one of the numbers by 100 and dividing the other one by 100 when you switch X and Y