How to reduce App (.apk) Size

Make sure that your jpg's aren't stored in any higher resolution than necessary. A nice Android phone has a screen resolution of 1920x1200 or 2560x1440 (circa 2015)800 x 480 , so your backgrounds shouldn't contain any more pixels than that (unless your app supports some kind of zooming). Also, are the backgrounds photographs? If not, you may find that using a vector based image format like svg, or one with a dynamic palette like gif, will reduce the file size even more.

Other answers mention shrinking images. You might also consider trying ProGuard to shrink your bytecode. Here's an article on applying ProGuard to an Android app.

I would recommend that you compress the .jpg files as much as possible, this should greatly reduce the size of your .apk file. A tool such as Paint.NET which is free should help you do this. It has great resizing options.