1. PDF is to a large extent is compressed Postscript. So would not get any compression program to compress it further or only a little.
2. As extension of PDF, most modern browser is able open it for online read.
3. The zip extension is too wintel centric.
Every operating system I know of these days supports .zip files because they have been around so long. For example on my Mac it opens them just by double-clicking. And when I RH-click and select "compress X" it produces a .zip file.
As a comparison I took disp11e.pdf (one of the ABC cards) which is 142 kB. I zipped it (on the Mac) and got 85 kB. So, almost half.
40% is not a little, good catch. normal pdf to a large extent is compressed Postscript, like ebook from publisher. compress it further do recieve that much gain. however pdf support much more object other than text. i.e. font, image... at OP case is pdf with embed image.
average zip compress ratio at jpeg is 20-25%. here is 40%. some fine tune might need. This the question for OP, What is app you use?
edit object images at this pdf,