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

It becomes clearer when you translate the words “per” and “of” into their mathematical operations. “per” means division and “of” means multiplication. Then it becomes straight-up algebra:

X% of Y

(X per 100) of Y

X
—- * Y
100

X * Y
——–
100

You get the same exact thing if you start the other way around:

Y% of X

Y
—- * X
100

Y * X
——–
100

Answer 2

It becomes clearer when you translate the words “per” and “of” into their mathematical operations. “per” means division and “of” means multiplication. Then it becomes straight-up algebra:

X% of Y

(X per 100) of Y

X
—- * Y
100

X * Y
——–
100

You get the same exact thing if you start the other way around:

Y% of X

Y
—- * X
100

Y * X
——–
100