All things being equal

One of my colleagues scribbled down their working to this question today:

Find 60% of $40.

Their solution was

10% = $4

60% = $24

To which a flashing red light went off in my head and I asked him why he was abusing the equals sign with his Carole Vordaman sums?! This then led to a public discussion over whether we should care about this sort of thing or whether it was just mathematical pedantry. Some of my colleagues suggested they wouldn't pull up students regarding this, as it's clear what they mean. Others opted to say that they wouldn't pull up weaker/less able students on this sort of thing.

Is this right? And does it even matter?

I tried to find a suitable analogy and all I could think of was an example of missing a capital letter at the start of your sentences in English. I'm not sure this is quite the same though. Unfortunately I haven't found a better one.

The analogy falls down in that capital letters in English are a useful convention to help signify the start of the sentence but I'm not sure they signify any deeper conceptual understanding. However, in this case there seem to be two concepts signified by the correct notation.

10% of $40 = $4 

or 

10% x $40 = $4

Firstly, there is the understanding that the equals sign represents balance (equality) between the two statements either side of it. Secondly, and perhaps more importantly, the correct use shows an understanding that you are taking a percentage of an amount, not just writing an equivalent form of the percentage.

For example, 40% = 0.4, is  a valid statement.

Is it not also important to realise that 10% = $4 is utter nonsense? Much like the sentence, Cat sat stood mat, makes little sense and in fact contains a contradiction.

Here's the question. Given that we know the statement is mathematically wrong is it important enough to challenge the misconception with our students? Should we worry when a Maths Teacher writes this in their working, or on the whiteboard? Or is that just Mathematical Pedantry? And does challenging the misconception lead to any better mathematical understanding anyway?

The incorrect use may not even signify an underlying misconception in some cases. I have no doubt, for example, that my colleague fully understands percentages of amounts.

So does it even matter?

If it does matter, should we tackle the misconception with all our students, or only with the most able? Is this something we shouldn't worry about in Y7 but should be concerned about in Y11? If so, at what point is it important to start challenging this misconception?

I'm keen to hear what other Maths Teachers think about this...