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I didn't spot this trick until I read this:

LPT: X percent of Y is equal to Y percent of X.

I know that multiplication is commutative; obviously, $\dfrac{X}{100}Y= X\dfrac{Y}{100}$. But this algebra doesn't betray the intuition that I feel I'm missing? How can this be intuited?

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    Because both are equal to $XY$ percentage of $1$? – dxiv Sep 14 '18 at 04:19
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    I think fix my intuition questions are outside the scope of SO maths – Paul Childs Sep 14 '18 at 04:32
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    @PaulChilds We get them fairly often and don’t tend to close them, and in my opinion they are fun and mentally stimulating. I would rather see eight of these than a single here’s-a-textbook-problem-I-couldn’t-do post. – gen-ℤ ready to perish Sep 14 '18 at 05:07
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    percent implies a part of number, so intuitively speaking and wlog, a small part of a large number is the large part of the small number. – farruhota Sep 14 '18 at 09:31
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    I think intuition questions are one of the most valuable parts of math.stackexchange. Developing intuitive understanding is one of the main challenges of learning math, is it not. I know I have often read a proof in a textbook which seemed terribly unmotivated, only to realize a year or two later that the proof is "obvious" once you see it from the right viewpoint. Such intuition is often missing from textbooks, but thankfully you can find it on math.stackexchange. – littleO Apr 11 '20 at 08:07

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Say,You have $$ 5\%~~of~~1000$ $$

So,here, $$x=5~~and~~y=1000$$ So,you have $$5\$~~in~~100\$$$ $$And, 50\$~~in~~1000\$ $$

Now,let's say you have $$1000\%~~ of~~5\$$$ So,this time also $$x=5~~and~~y=1000~~~[according~to~your~strategy]$$

But now notice carefully..what is it saying?this time it is enlarging the 5$.How?

this means- $$ by~~100\$~~we~~have~~1000\$ $$ hence,$$by~~5\$~~we~~have~~50\$ $$

Rakibul Islam Prince
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