Calculating VAT Percentage Fraction

Calculating VAT Percentage Fraction

The VAT Fraction

The VAT fraction of 7/47, is arrived at by converting the decimal fraction of 0.175/1.175 to the lowest whole numbers(simple fraction).

If VAT is at 5%, the VAT fraction would become 1/21 (which is just the whole number equivalent of the decimal fraction 0.05/1.05).

If VAT is at 15%, the VAT fraction would become 3/23 (which is just the whole number equivalent of the decimal fraction 0.15/1.15).

If VAT is at 17.5%, the VAT fraction would become 7/47 (which is just the whole number equivalent of the decimal fraction 0.175/1.175).

Calculating VAT Percentage Fraction - Example

Lets assume we wish to find the VAT fraction for 12.50%.

1. The numerator (top half of fraction) is derived by simply taking the VAT percentage and dividing by 100.
   
   12.50  ÷  100  =  0.125
   
   
2. The denominator (bottom half of fraction) is derived by simply taking the VAT percentage and dividing by 100, then adding 1.
   
   (12.50  ÷  100)  +  1  =  1.125
   
   
3. The numerator and denominator are then multiplied by 1000 to remove the decimal point.
   
   0.125  x  1000  =  125
   1.125  x  1000  =  1125
   
   

How To Simplify

Perhaps you think that fractions can never be simple, but they can often be written more simply.

The way to simplify fractions is to make the top and bottom numbers smaller.  You can only do this by finding a number that divides into them.  Any other method would change the value of the fraction.

The important thing is that you must find a number that divides into both the top and bottom numbers at the same time.  This is sometimes called cancelling down.

This is the case with the fraction above.  You can divide the top and bottom of each one by the number that happens to be on the top.  Let's check how this works with 125 / 1125. We can divide both numbers by 5.

For the top number(numerator):-

125  ÷  5  =  25

For the bottom number(denominator):-

1125  ÷  5  =  225

However, this can still be cancelled down further.

Thus:-

For the top number(numerator):-

25  ÷  5  =  5

For the bottom number(denominator):-

225  ÷  5  =  45

However, this can still be cancelled down further.

Thus:-

For the top number(numerator):-

5  ÷  5  =  1

For the bottom number(denominator):-

45  ÷  5  =  9

Thus in conclusion; 12.50% is 1 over 9 as a fraction.

How To Simplify Using Microsoft Excel

1. Having completed steps 1 - 3 above, place both figures into a cell like so:  =SUM(125/1125)
2. Select the cell you want to format.
3. On the Format menu, click Cells, and then click the Number tab.
4. In the Category list, click Fraction, and then click the type of fraction you want to use.

Decimal - VAT Fraction Conversion Table

The VAT fraction table below contains all VAT fractions from 0.25% thru 30.00% at increments of 0.25.   Key rates are highlighted in red.

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