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
Percent (the sign of percent is %) means the number of something per 100, so 5 percent is 5 per 100, 1 percent is 1 per 100, 100 percent is 100 per 100.
Per is the same as splitting something up:
100 percent = 100 cakes split up between 100 people = 1 cake each
50 percent = 50 cakes split up between 100 = half a cake each
10 percent = 10 cakes split up between 100 = a 10th of a cake each
Remember that percent means 1 per 100.
So 20 percent (20 times 1 cake split up between 100) becomes “20 times 1 per 100” and 40 percent becomes “40 times 1 per 100”
We write it like this:
20 percent of 40 cakes = 20 * 1/100 * 40 cakes = 8 cakes
40 percent of 20 cakes = 40 * 1/100 * 20 cakes = 8 cakes
You can see that they are the same, well remember 2 + 1 is the same as 1 + 2 & 1 * 2 is the same as 2 * 1; you can move these numbers around a bit.
So 40 * 20 * 1/100 = 8
and 1/100 * 20 * 40 = 8
Lets stop talking about cake.
20 * 1/100 * 40 = 8
40 * 1/100 * 20 = 8
And turn 1/100 back into the percent sign % from the start
20% of 40 = 8
40% of 20 = 8
X% of Y = Y% of X
Lets say there are two numbers
X and Y
To get X% of Y
we’ll have,
X * (Y/100)
=(X*Y)/100
let this be equation 1.
Now lets say for getting Y% of X,
we’ll do Y * (X/100)
= (Y*X)/100
this our equation 2.
You see, equation 1 and equation 2 are same.
just X and Y are swapped.
so when you say 5% of 10.
you do 5*(10/100)
but when you say 10% of 5.
you do 10*(5/100).
but both will give same answer
50/100
Think of it this way. Let’s take 25 percent of 3. We’ll you can write this as 0.25 x 3
Now flip it. 3 percent of 25. Well that’s just 0.03 X 25. They’re the same thing! Just a factor of 100 different both sides.
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
Percent (the sign of percent is %) means the number of something per 100, so 5 percent is 5 per 100, 1 percent is 1 per 100, 100 percent is 100 per 100.
Per is the same as splitting something up:
100 percent = 100 cakes split up between 100 people = 1 cake each
50 percent = 50 cakes split up between 100 = half a cake each
10 percent = 10 cakes split up between 100 = a 10th of a cake each
Remember that percent means 1 per 100.
So 20 percent (20 times 1 cake split up between 100) becomes “20 times 1 per 100” and 40 percent becomes “40 times 1 per 100”
We write it like this:
20 percent of 40 cakes = 20 * 1/100 * 40 cakes = 8 cakes
40 percent of 20 cakes = 40 * 1/100 * 20 cakes = 8 cakes
You can see that they are the same, well remember 2 + 1 is the same as 1 + 2 & 1 * 2 is the same as 2 * 1; you can move these numbers around a bit.
So 40 * 20 * 1/100 = 8
and 1/100 * 20 * 40 = 8
Lets stop talking about cake.
20 * 1/100 * 40 = 8
40 * 1/100 * 20 = 8
And turn 1/100 back into the percent sign % from the start
20% of 40 = 8
40% of 20 = 8
X% of Y = Y% of X
Lets say there are two numbers
X and Y
To get X% of Y
we’ll have,
X * (Y/100)
=(X*Y)/100
let this be equation 1.
Now lets say for getting Y% of X,
we’ll do Y * (X/100)
= (Y*X)/100
this our equation 2.
You see, equation 1 and equation 2 are same.
just X and Y are swapped.
so when you say 5% of 10.
you do 5*(10/100)
but when you say 10% of 5.
you do 10*(5/100).
but both will give same answer
50/100
Think of it this way. Let’s take 25 percent of 3. We’ll you can write this as 0.25 x 3
Now flip it. 3 percent of 25. Well that’s just 0.03 X 25. They’re the same thing! Just a factor of 100 different both sides.
Latest Answers