Is 20% of 50 the same as 50% of 20?

Do you ever think that 20% of 50 is the same as 50% of 20? At first, they looked different. But surprisingly, they give the exact same result! But how???

HERE IS THE SIMPLE CALCULATION:

Let’s start with both calculations:

• 20% of 50 = $\frac{\mathrm{<b>20</b>}}{\mathrm{<b>100</b>}}<b>\times </b>\mathrm{<b>50</b>}$

• 50% of 20 = $\frac{\mathrm{<b>50</b>}}{\mathrm{<b>100</b>}}<b>\times </b>\mathrm{<b>20</b>}<b>=</b>$

✅ The answer is 10 in both cases. But this is not just a coincidence. It works with other numbers. 

BUT BUT BUT, MATHEMATICALLY WHY THIS HAPPENS? 

Mathematically, A% of B means: 

$\frac{\mathrm{<span\; style="font-size:\; small;"> A</span>}}{\mathrm{<span\; style="font-size:\; small;"> 100</span>}}<span\; style="font-size:\; small;">\times B</span><br>$

Similarly, B% of A means:

$\frac{\mathrm{<span\; style="font-size:\; small;">B</span>}}{\mathrm{<span\; style="font-size:\; small;">100</span>}}<span\; style="font-size:\; small;">\times </span>\mathrm{<span\; style="font-size:\; small;">A</span><span\; style="font-size:\; small;"><br></span>}$

$$\frac{A}{100} \times B = \frac{B}{100} \times A$$

This is true because of the commutative property of multiplication. Here, Changing the order of numbers in multiplication doesn’t change the result. That is, A×B=B×A

WILL THIS ALWAYS BE TRUE???

The answer is Yes. This is true for any real number (integers, negative numbers, decimals, fractions, etc) of A and B. No matter what the values are, the result is always the same. Such as,

1. 10% of 30 = 3, and 30% of 10 = 3

2. 5% of 80 = 4, and 80% of 5 = 4

3. 2% of 500 = 10, and 500% of 2 = 10

4. 25% of 80 = 20, and 80% of 25 = 20

5. 12% of 75 = 9, and 75% of 12 = 9

6. 7.5% of 40 =3, and 40% of 7.5 = 3

FINAL NOTE: 

A% of B is equal to B% of A.