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
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
“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.
X% of Y = Y% of X. A percentage is a multiplication. Like 69% of 70 = 70×0.69. So:
Y × X/100 = X × Y/100 //×100
Y × X = X × Y
True because multiplication is commutative.
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
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
“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.
X% of Y = Y% of X. A percentage is a multiplication. Like 69% of 70 = 70×0.69. So:
Y × X/100 = X × Y/100 //×100
Y × X = X × Y
True because multiplication is commutative.
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