It’s important when demonstrating mathematical procedures that you stress the mathematics behind those procedures (i.e., the “why” behind the “what” or “how”), since failing to do so can cause or reinforce students’ misconceptions. Take, for example, multiplying fractions, as in the case of 3/5 x 5/8. Commonly—and correctly—teachers note that “the fives cancel out,” leaving 3/8 as the product.
The problem is that unless students understand why the fives cancel out, they see it as some mechanical (if not magical) step in the process. A common mistake, among others, I’ve seen students make as a result has been to also cancel out when adding or subtracting fractions—such that the sum of 3/5 and 5/8 would then equal the product of 3/5 and 5/8. To prevent this and other related errors, explain the mathematical basis for cancelling—i.e., you’re not really cancelling common factors, but rather dividing them to yield a quotient of 1 (represented as 1/1). Then show students (or better yet, have them discover themselves) that while this works when multiplying fractions, it doesn’t work when adding or subtracting them.
Is it ever ok to mutter “cancel out the 5s” as you work through a problem or just execute the cancellation without a word like your teachers may have done? Sure, once you’ve prevented or alleviated any misconceptions related to this. But until then, cancel out “cancel out,” and instead talk to students about the math behind it.