There are so many maths mistakes you have made in your post that I will have to illustrate them one by one. Sorry if this sounds crude but I just want you to understand armor in a correct way.
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FIFY.
Let's do an example. We'll use my main, amumu (base armor at level 18 = 88.1, we round to 88 for convenience, http://leagueoflegends.wikia.com/wiki/List_of_champions'_armor).
My standard rune and mastery set gives me 9 bonus armor and 5% bonus armor/mr and my standard build is as follows:
6th item is flex, lets ignore that for now.
My total armor from this build is 88 + 9 + 30 + 50 = 177 x 1.05 = 179.5 ~ 180
Of this 180 total armor, 88 is base, and 92 is bonus.
First of all, Unyielding (the mastery that increases armor) only increases bonus armor, so only 89 armor should be taken into consideration in terms of Unyielding.
Total armor should be instead 88 + 9 + 30 + 50 + (89 x 0.05) = 181.45 ≈ 181
Base armor = 88
Bonus armor = 181 - 88 = 93
I don't agree with your way of rounding off because it leads to inaccurate and flawed calculation but for the sake of this piece of maths, I will let it go.
Now let's move onto the penetration stats:
(max 30% armor shred): 180 x .70 = 126 total armor, of which only 38 is bonus armor (126 - 88 = 38)
Second, like I replied to you in a previous post, armor reduction, for instance The Black Cleaver, shreds both base and bonus armor, so if you say the resulting bonus armor is 38. You are very wrong.
For the sake of it, I'll keep the wrong maths in part 1 (calculation for total armor) and use it for part 2 (calculation for resulting armor after armor reduction from The Black Cleaver):
The resultant total armor after the shred of The Black Cleaver (max stacks) = 180 x 0.7 = 126
The remaining base armor = 88 x 0.7 = 61.6 ≈ 62
The remaining bonus armor = 92 x 0.7 = 64.4 ≈ 64
If we use the right maths in Part 1:
The resultant total armor after the shred of The Black Cleaver (max stacks) = 181 x 0.7 = 126.7 = 127
The remaining base armor = 88 x 0.7 = 61.6 ≈ 62
The remaining bonus armor = 93 x 0.7 = 65.1 ≈ 65
or
(45% penetration to BONUS armor): 38 x .45 = 17.1 ~ 17 armor pen
The 7% pen from masteries will still act on the 126 armor stat, as the actual armor value remains unchanged by the LW item, so
126 x 0.07 = 8.82 ~ 9 amor pen.
Third, percentage armor penetration stacks multiplicatively (whether it's total armor penetration or bonus armor penetration), so your maths here are very off.
For the sake of clarity, let's use the correct version of Part 2, shall we?
The remaining base armor after considering all sources of armor penetration (LW upgrade and Battering Blows) = 62 x 0.93 = 57.66 ≈ 58
The remaining bonus armor after considering all sources of armor penetration (LW upgrade and Battering Blows) = 65 x 0.93 x 0.55 = 33.2475 ≈ 33
The resultant total armor = 58 + 33 = 91
Now let's figure out the total % of armor ignored.
(126 armor after cleaver shred) - (17 armor from LW item) - (9 armor from mastery) = 100 effective armor
total starting armor was 180, so (100/180) = 55.5 ~ 56% of starting armor meaning that max possible armor ignored with items is 44% NOT 64%.
Last but not least, let's find out the true value of total armor ignored (After rounding the numbers off for the millionth time, I doubt it's the truest value but whatever):
Armor reduced and penetrated = 181 - 91 = 90
Percentage of total armor reduced and penetrated = 90 / 181 = 49.723% ≈ 50%
Conclusively around 50% of armor is ignored in total.
As for percentage of base armor reduced and penetrated = (88 - 58) / 88 = 34.090% ≈ 34%
Percentage of bonus armor reduced and penetrated = (93 - 33) / 93 = 64.516% ≈ 65%
In conclusion, LankPants is right for the most parts, you on the other hand...
*I am Carol Peletier but I changed my name.