# Egyptian Fractions

## some thoughts...

The VAT rate is at present 17·5%.

To calculate the VAT on, say, £150, we need to work out (17·5 x 150)/100 = £26·50.

We could also do it as 17·5 x 1·5 or as 17 ½ x 1 ½.

Then again, if we notice that 17·5 = 10 + 5 + 2·5, we can simplify the working for pencil and paper as

**10% of 150** | is** £15·00** |

**5% is half 10%** | or **£7·50** |

**2·5% is half of 5%** | or **£3·75** |

**add these results** | to get** £26·25** |

This method was usually called "Practice" and is very useful for calculations in Imperial units, (or pre-metric units in other countries).

2·5% is also sixpence ^{(1)} in the pound, so 17·5% is 7 sixpences in the pound, and we could, if we wanted to, calculate the answer as 7 x 150 sixpences = 7 x 75s = 525s = £26.5s.0d.

Sixpence is a fortieth of a pound, so what we are really doing is expressing the fraction 7/40 as 1/10 + 1/20 + 1/40, which is what the Ancient Egyptians would have done.

So are the methods found in the Egyptian scrolls really recipes for doing sums by Practice methods?

^{(1)} 6d, not 6p...