# Percentages Are Reversible

What do we mean by

**reversible**?

We're asked what is

**20%**of

**50**.

We could reverse the numbers to make the problem a bit easier.

That is,

**50%**of

**20**is the same as

**20%**of

**50**.

Why are they reversible? Seems like magic, but it's far from it.

It's actually simple.

**Percentage means per hundred**.

Whenever we see a percentage, we can replace it with

**(1/100)**or

**.01**.

So, when we are asked what is

**20%**of

**50**we are really doing

**2 multiplications**.

**20 * 50 * .01 = 10**

### Key Takeaways

Multiplication is Commutative.

Commutative means that order doesn't matter.

**a * b = b * a**

An example of an operation that is not commutative is subtraction.

**a - b != b - a**

Therefore, sense taking a percentage is just two multiplications, and a **percentage is .01** it doesn't matter which order we do our operations.

**(20 * .01) * 50 = 20 * (50 * .01) = 10**

### Conclusion

Reversing a percentage may not always make the problem easier, for example
**7% of 13** and **13% of 7** are about equally difficult to solve without a calculator.

However, in some problems it can make life simpler, but what is more important is for us to understand what a percentage really is and why we can reverse it.

Often times in mathematics, and in life, if we really understand a problem, we can rearrange it to our advantage.

### Resources