Comma and arithmetics

Should one put a comma before an arithmetic operation? What about long expressions?

Example: The final distance is equal to the initial distance plus initial velocity multiplied by time, plus half the acceleration multiplied by the square of time.

• When it serves to disambiguate, punctuation is always a good thing. In your example, it does: it lets you know it's not [initial velocity] multiplied by [time plus half the acceleration] multiplied by Times Square. Apr 2, 2015 at 13:53
• The final distance is equal to the initial distance plus initial velocity multiplied by time, plus half the acceleration multiplied by the square of time. would possibly be read as The final distance is equal to (the initial distance plus initial velocity) multiplied by time, plus half the acceleration multiplied by the square of time. Dimensionally unsound, but ELU doesn't address such issues. The correct ways of expressing equations are function or flow-diagram formats.... Apr 2, 2015 at 13:53
• Maths has developed the necessary discriminatory equipment; English really hasn't (unless brackets are used in the mathematical way, which becomes unwieldy). Apr 2, 2015 at 13:53

3 Answers

The secret to writing about mathematical equations is to describe the equation as a whole. I would do it this way:

The final distance is equal to the sum of three parts: 1. the initial distance, 2. initial velocity multiplied by time, and 3. half of the acceleration multiplied by the square of time.

Whenever possible, I would follow the written description by showing the equation.

There's a reason equations are best represented by symbols. I don't think mere punctuating it correctly will see you all the way through. I must suggest paraphrasing:

The final distance is equal to the initial distance added to the sum of the initial velocity multiplied by the time taken and half the acceleration multiplied by the square of the time taken.

As Edwin pointed out in his comment, commas aren't gonna cut it, you'll have to bring brackets into the mix to avoid ambiguity. And since the usage of brackets in English and in math is vastly different, it would look odd.

I would be extra careful about this, in many European countries you write one-thousand and 2/10ths as follows:

1.000,2

And In North America:

1,000.2

If you want tot write five-thousand Francs:

₣5.000

But you write five thousand dollars,

\$5,000

Thus the arithmetic operations get complicated if you do not obey the cultural norms.