# Properly working with GST (or any other percentage) Part 2

In order to explain why this works, some maths is needed. Don’t go to sleep! If the thought of maths gives you sudden-onset narcolepsy, then just know this:

To go from ex GST to inc GST correctly, divide your ex GST amount by 0.9

Ok! Now if you’re still with me, let’s go through why this works. To explain this, I’m going to assume you understand how to use percentages in sums. A percentage is a number between 0 and 1, i.e. 10% is 0.1, 20% is 0.2 and so on. The bit below will use numbers only, not percentages.

A key thing when working with any formula is the formula works both ways, you just reverse the steps and operators. For example, 2+3 = 5. This works both ways: if we reverse the formula, start with Five, take Three, we get Two, i.e. 5-3 = 2. By going through the formula forwards and back, and ending up with the same numbers, we know the formula works.

So, with that principle in mind, let’s start from an inc GST amount of \$110. To go from inc to ex:

110×0.1 = 11

110-11 = 99

A one-step process to work this out is: rather than work out 10% and then subtract that from the 100%, just look for the remaining 90% straight up. And so:

110×0.9 = 99

Now, knowing that a formula works both ways, just by reversing the steps and operators, we can go from 99 to 110 in one step:

99÷0.9 = 110

And this is how we calculate an inc GST price from an ex GST price, accurately and in one step!

## How to use this process for any percentage amount

If you’ve followed the reasoning’s above, then this should be fairly simple. Take your percentage amount from 1, and use that as your number to multiply/divide as needed. Here’s a worked example:

Let’s say you use PayPal to receive payments from customers. Paypal charges 2.6% on the amount paid by the customer. You want to include that 2.6% in your fees, so the customer covers the cost and not you. The number you need is:

1-0.026 = 0.976

The shirts you sell, inc GST, are \$110. You want to make sure the customer pays an amount that covers the shirt cost and PayPal fees. How much do you charge the customer?

110÷0.976 = 112.7049

You charge the customer \$112.71 (rounded up). To make sure this works, take your price inclusive of PayPal feesand remove the 2.6%:

112.71×0.976 = 110.00496

With that rounded, you get \$110 and the same number. Excellent!