Not Everything That Matches will Cancel

Often we cancel things in expressions and equations. But not everything that matches will cancel!This is Day 5 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

I do or die, but I never cancel out.
~Pat Nixon

“Cancelling” is a sloppy math word for undo.

Well, undo is also a sloppy math word. But it more clearly represents what happens when we cancel things properly.

To cancel something, you’re really making 1 or making 0.

For example, to reduce the fraction 12/42, we can “cancel” 6 from both the top and bottom.

Like this:


However, what’s really happening is some “undoing” of multiplication and then making 1.


That’s a really long way to write it. But writing it the long way helps to see that it actually works – with some true-blue math rules. Not tricks.

Things that Don’t Work

Let’s look at the things that won’t cancel, but look like they will.

Bad cancelling
(this isn’t true, by the way – logs can’t cancel like this)

There’s a temptation to cancel the “log” parts. But logarithm is an operation (like addition or division). So canceling logs is like canceling the plus sign here:

bad cancelling
(also untrue)

And sometimes we get excited and want to cancel pieces of a fraction like this:

bad canceling
(yipes, more bad canceling)

But that doesn’t work because there are implied parenthesis,so you need the distributive property.

Do it the long way to confirm.

It’s easy for a math teacher to say, “All you have to do is cancel these.” But if you doubt what she says, do it the long way.

Tricks aren’t helpful if they mix you up. And if you mix up tricks, it’s even worse.

Take a moment to do it the long way.

And if you need support, join the Facebook group for parents – we’re here to help!


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