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Being physics trained, we would do a problem like this:

$v=\frac{d}t$

$ =\frac{2 m}{4 s}$

$ =0.5 ms^{-1}$

Of course, being physics trained, we didn't always hold to the full conventions of mathematics. However, I am now being told to teach the problem like this:

$v=\frac{d}t$

$ =\frac{2}{4}$

$ =0.5 ms^{-1}$

That is, without the units in the problem until the end. Now I argue that the units help see where mistakes can occur - you can follow the units as a quick path to find where an error has crept in. However, I have been told that it is "not mathematical convention" to use units throughout. Is that correct? If so, why?

Brendan
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    In my opinion, you’re “being told” wrong. I would prefer to keep the units throughout. – Lubin May 21 '21 at 01:54
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    @Lubin is right, +1. That’s just plain sloppy and not rigorous. Either keep the units everywhere, or omit them everywhere. You can say that $d$ is the distance measured in meters, or you can say that $d$ is the distance. The first would be $d=2$, the second would be $d=2;m$. – MPW May 21 '21 at 02:07
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    I would say that the second method is okay if you feel your students have reached a certain level of comfort with units, perhaps used for second/third examples of a new procedure. But the first method is the default, eliminates confusion, highlights errors, etc. – Greg Martin May 21 '21 at 02:20
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    “Highlights errors” indeed, @GregMartin. You can see at a glance when you’re adding things with different units, or when your answer has the wrong units. – Lubin May 21 '21 at 02:23

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