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VAT fraction.

  • 16 posts
  • # 87569

Can anyone showed me how to calculate 17.5% VAT to fraction 7/47? Thank you.
Lesley
  • 116 posts
  • # 87575

Hi Rimmelly952

You take the gross amount i.e. 250.00 divide by 47 then times by 7 = £37.234042 which becomes £37.23

You then deduct the vat from the gross to get a net figure of £212.77

If you work back the way and add 17.5% to £212.77 you will get £250 which is a good way of checking your figures are correct.

Hope this helps.

Lesley
  • 16 posts
  • # 87583

Thank you very mcuh Lesley for your reply, much appreciated. 

I just want to know how the calculation reach to fraction 7/47  for 17.5% Vat ; 1/6 for 20% Vat ; 1/21  for 5% VAt.

Say 1/6 the calculation 100/120 =5/6 so 20% VAT  20/120 =1/6 just guessing

Say 1/21 the calculation 100/105 = 20/21 so 5%VAT 5/105 =1/21 just guessing for both computations.

Can anybody confirm please that is correct?
 
 But cannot seemed to get the calculation for 7/47 (17.5VAt) 
Lesley
  • 116 posts
  • # 87584

sorry I must have misunderstood your question.

To be honest Im not sure how this one is worked out...maybe someone else on here can enlighten us!
Brianh
  • 56 posts
  • # 87588

Hi Rimmelly952

At a rate of VAT 17.5%:

Exclusive of VAT = 200

VAT                          = 35

Inclusive of VAT   = 235

 

To extract VAT from VAT inclusive amount  fraction is 35/235

This is scaled to 7/47 (divide numerator and denominator – top and bottom numbers of the ‘big’ fraction by 5 to bring it to its lowest terms)

 

 

At a rate of VAT 20%:

Exclusive of VAT = 200

VAT                          = 40

Inclusive of VAT   = 240

 

To extract VAT from VAT inclusive amount  fraction is 40/240

This is scaled to 1/6 (divide numerator and denominator – top and bottom numbers of the ‘big’ fraction by 40 to bring it to its lowest terms)

 

At a rate of VAT 5%:

Exclusive of VAT = 200

VAT                          = 10

Inclusive of VAT   = 210

 

To extract VAT from VAT inclusive amount  fraction is 10/210

This is scaled to 1/21 (divide numerator and denominator – top and bottom numbers of the ‘big’ fraction by 10 to bring it to its lowest terms)


Kind regards
Brian  
Lady of Ledger
  • 491 posts
  • # 87594

Or some find it easier to use the following methods for calculations...


17.5% (1.175) gross to net = divide by 1.175  i.e. £235 divided by 1.175 = £200
 
17.5% net to gross = multiply by 1.175 i.e. £200 multiplied by 1.175 = £235


20% (1.20) works on the same principle - use 1.2 i.e. £240 divided by 1.2 = £200  £200 mutiplied by 1.2 = £240


5% (1.05) works on the same principle - use 1.05 as your figure to divide or multiply by


Hope this helps

Carol         

  • Carol Saunders
    Lady of Ledger Book Keeping
    Telford, Shropshire



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  • 16 posts
  • # 87601

thank you very much Brian and Carol for your reply, very much appreaciated BUT my question stil unanswered.
 
 
My question is why is it that 17.5 % Vat has a fraction of 7/47 that can be used to calculate the amount of VAT included in an item at 17.5% =7/47.  ;from what number does 7/47 comes from?
Timm
  • 88 posts
  • # 87604

17.5% is not a number, but a formatted symbolic repersentation of a number. You need to convert the % to a  fraction to do the maths.
The VAT Fraction= Rate of VAT/ 100+rate of VAT
e.g. Todays standard rate of VAT is 20% so 20/100+20 = 20/120 = 8/48

 
Lady of Ledger
  • 491 posts
  • # 87605

Because it's the lowest common denominator of the fraction of 17.5 divided by 117.5 (VAT rate divided by 100 plus VAT Rate)

For example - 2.5 is the lowest common denominator here, because it's the lowest figure that will divide into both the top part of the fraction and the bottom part of the fraction.

So the fraction is dealt with
...... 17.5 divided by 2.5 = 7
.......117.5 divided by 2.5 = 47 

hence the fraction 7/47

If £117.50 is multiplied by 7, then divided by 47 - you get the rate of VAT applied in that figure - £17.50

If £117.50 is multiplied by 17.50, then divided by 117.50 - you get the rate of VAT applied in that figure - £17.50

It's just 'reducing' the fraction down  to what most  feel is a more manageable figure to use.

Hope that answers it................:-)

Carol  

  • Carol Saunders
    Lady of Ledger Book Keeping
    Telford, Shropshire



  • Quote
  • 16 posts
  • # 87616

Carol thank you very much for the explanation, my question has  now been answered, very much appreciated. thank you!
  • 16 posts
  • # 87617

Timmsaid:

“17.5% is not a number, but a formatted symbolic repersentation of a number. You need to convert the % to a  fraction to do the maths.
The VAT Fraction= Rate of VAT/ 100+rate of VAT
e.g. Todays standard rate of VAT is 20% so 20/100+20 = 20/120 = 8/48

 ”

thank you Timm!
eboakye
  • 18 posts
  • # 87619

17.5% is 17.5/100 which is 175/1000; which is 7/40.  Hope this helps
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