The terms elaborative and maintenance rehearsal has two different meanings, but despite their differences they can also be used simultaneously. In another words, by means of maintenance rehearsal you can also practice elaborative rehearsal as well. The basic and simple mental repetition of information defines mental rehearsal, while focusing on the meaning of information or relating it to other things we already know explains elaborative rehearsal. The purpose of rehearsing information is to extend its duration in short-term memory.
At least once or twice a day you will look up someone's number via your phone book or a torn piece of paper with numbers scribbled on it. Usually before you dial the number in the process of waiting in line to use the phone, you would probably find yourself repeating the numeric order a few times aloud on silently just to make sure you are dialing the right number. The act of repeating the number exhibits mental rehearsal. If the numbers have a certain familiarity to it or if it reminds you of something else like someone else's number, this in turn illustrate elaborative rehearsal. You use mental rehearsal to temporarily memorize the number and that could lead or trigger some other type of memory relative to it, thus elaborative rehearsal.
Another common example would be when you are trying to memorize vocabulary words for an upcoming vocabulary quiz or test. Typically you would repeat the word and then the definition a few times. Then afterwards you would try to cover it up and recite the definition trying hard not to "peak" at the answer. Then in the end or so you would try to think of shortcuts or mnemonics to help you figure out how to remember the words. Thus both mental and elaborative rehearsals are performed.
Especially in mathematics, you will memorize formulas because your professor thinks it is too easy to hand you a cheat sheet and/or for the sake of efficiency.