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

“Percent” means “per 100”. You can write 25% as 25 / 100 or 25 x 1/100.

If you write it as 25 x 1/100, its pretty obvious that you’re just multiplying two numbers. X percent is just X x 1/100.

When you multiple numbers, the order that you multiply them doesn’t matter; you get the same results (2 x 3) x 4 = 2 x (3 x 4) = (2 x 4) x 3 = 24. You can visualize that with pennies: 4 groups of pennies laid out in 2 rows and 3 columns, or 2 groups of pennies laid out in 3 rows and 4 columns, etc.

So now X% x Y = X x Y% because the ‘%’ symbol means ‘x 1/100’: X x 1/100 x Y = X x Y x 1/100 — because the order you multiple the 3 numbers doesn’t matter.

Answer 2

“Percent” means “per 100”. You can write 25% as 25 / 100 or 25 x 1/100.

If you write it as 25 x 1/100, its pretty obvious that you’re just multiplying two numbers. X percent is just X x 1/100.

When you multiple numbers, the order that you multiply them doesn’t matter; you get the same results (2 x 3) x 4 = 2 x (3 x 4) = (2 x 4) x 3 = 24. You can visualize that with pennies: 4 groups of pennies laid out in 2 rows and 3 columns, or 2 groups of pennies laid out in 3 rows and 4 columns, etc.

So now X% x Y = X x Y% because the ‘%’ symbol means ‘x 1/100’: X x 1/100 x Y = X x Y x 1/100 — because the order you multiple the 3 numbers doesn’t matter.