8 November 2013

Calculations
From the old divisor obtained from the templates:
 $ {div}_{\text{old}} = 10.0000 $
We need to calculate a new divisor:
 $ {div}_{\text{new}} = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} $
To calculate the new divisor, we need to find:
 $ \begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{280}{34} + \frac{399}{40} + \frac{123}{18} + \dots + \frac{1,646}{1,221} \\ & = 32.08119681 \text{ (up to 8 d.p.)} \end{align} $
And also:
 $ \begin{align} \sum \left ( \frac{p}{q} \right )_{\text{new}} & = \text{sum of ratios prior to change}  \text{sum of removed ratios} + \text{sum of added ratios} \\ & = \sum \left ( \frac{p}{q} \right )_{\text{old}}  \text{sum of removed ratios} + \text{number of added items} \\ & = 32.08119681  0 + 1 \\ & = 33.08119681 \text{ (up to 8 d.p.)} \end{align} $
Thus, the new divisor is:
 $ \begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 10.0000 \times \frac{33.08119681}{32.08119681} \\ & = 10.3117 \text{ (4 d.p.)} \end{align} $

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