Calculation of percentage value through Addition

Calculation of percentage value through Addition

It is the best understandable by an example.

Example:
What is the percentage value of the ratio: $$\frac{{53}}{{81}}$$

Solution:
This process is based on 100%, 50%, 10%, 1%, 0.1 % and so forth values of the denominator from the numerator.
$$\frac{{53}}{{81}}$$ can be rewritten as,
\eqalign{ & = \frac{{40.5 + 12.5}}{{81}} \cr & = \frac{{40.5}}{{81}} + \frac{{12.5}}{{81}} \cr & = 50\% + \frac{{12.5}}{{81}} \cr & = 50\% + \frac{{8.1 + 4.4}}{{81}} \cr & = 50\% + 10\% + \frac{{4.4}}{{81}} \cr & = 60\% + \frac{{4.4}}{{81}} \cr}
At this stage we can understand that the answer to the question lies between 60 - 70% (since 4.4 is less than 10% of 81). The answer would be in this form, 6a.abcd....
In order to find the percentage value of $$\frac{{4.4}}{{81}}$$, we can find it,
% value of $$\frac{{4.4}}{{81}} = 4.4 \times \frac{{100}}{{81}} = \frac{{440}}{{81}}.$$     (Here we get 5 % with remainder 35)
b = $$\frac{{350}}{{81}}$$ = 4 remainder 26.
c = $$\frac{{260}}{{100}}$$ = 3 remainder 17 and so on.

Calculations of Multiplication by Numbers like 1.41, 0.83 and so on through addition

Example:
Calculate 1.23 × 473.

Solution:
One can view this multiplication as an addition of 23% to the original number. This means
473 × 1.23 = 473 + 23% of 473 = 473 + 94.6 + 3% of 473
= 567.6 + 14.19 = 581.