How to convert percentage values from 7 point scale to 5 point scale? Suppose in one year I had a survey with 7-point scale and the values are like
Scale7, 1: 28%
Scale7, 2: 12%
Scale7, 3: 10%
Scale7, 4: 15%
Scale7, 5: 15%
Scale7, 6: 10%
Scale7, 7: 10%

where % are the percentage of responses for each scale from the sample size.
Now for next year if I have survey on the same question but with 5-point scale like
Scale5, 1: 25%
Scale5, 2: 25%
Scale5, 3: 10%
Scale5, 4: 20%
Scale5, 5: 20%

where % are the percentage of responses for each scale from the sample size.
Then if I have to convert the 7 point scale responses to 5 point scale how do I do that?

To "translate" the scales, you would need to be able to make an assumption that the distributions of the underlying phenomenon did not change across time, the only difference was the measurement units that were used. Notice that this is a pretty strong assumption. If you can make it, you could use equating.
There are simpler approaches, but with tabular data like this, you could easily use equipercentile equating. If there are two distributions $F_X$ and $F_Y$, you could "translate" $X$'s by plugging the $F_X$ cumulative probabilities to the inverse of $Y$'s distribution $F_Y^{-1}$:
$$ \operatorname{Equi}_Y(x_i) = F^{-1}_Y \left[ F_X(x_i) \right] $$
or the same using a graphic

So what you need to do is to calculate the cumulative probabilities and align the values by matching their cumulative probabilities.




$y$
$Pr(Y\le y)$
$x$
$Pr(X\le x)$




1
28%
1
25%


2
40%




3
50%
2
50%




3
60%


4
65%




5
80%
4
80%


6
90%




7
100%
5
100%



