Matter and anti-matter cancels out (violently I might add). The airlines can cancel your flight. You can’t cancel out in Math (instead you “reduce” or “divide”). If you do try to cancel out, bad things can happen. Let me explain.
Our Department abolished the phrase “Cancels out” a long time ago, and now we use phrases such as “reduces to 1“, “divides to 1 over 1“, etc. which demonstrates the math operation not some magic. We also always replace numbers and variables that reduce with a number even if it’s one (see below right).
Here’s a great example of actual work I’ve seen (and I’m sure you have too) on the left. Although we don’t necessarily teach this example problem to be solved this way, students often use this method and I just want to illustrate what often happens if they think “cancels out“. What we teach is shown on the right.
If every teacher in your department does this (how you write it and how you say it), your students will quickly get used to it. Try it!
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