Question

D=M/V solve for V.

I know the answer is m/d but is there any other way to do it besides multiplying V so you would get

Dv=M then you divide by D on both sides but what if you multiply by M to get V by itself so

D=M/V so M/V*M cancels out M snd D*M is Dm=V

Why doesn’t that work?

Answer 1

Explanation:

The answer is no!

Your first result is the correct one. I think what that the problem is units

density is defined as mass / volume

so when you write the formula, you get

grams / cm^3

Now take a look at what you want to do. What are the units.

D = mass / volume

m = mass

If you put them together the way you did, you get

grams * grams which gives grams^2 / cm^3

=====

cm^3

gram^2/cm^3 gives no known result. There is nothing in the physical world defined that way

Sorry to disappoint you, but you have to stick to the tried and true.

Answer 2

Answer: See below

Explanation:

To solve for V, we want to first multiply both sides by V, then divide by D.

`D=(M)/(V)` [multiply both sides by V]

`DV=M` [divide both sides by D]

`V=(M)/(D)`

That is the correct answer.

You cannot multiply both sides by M because that would give you M². The whole point is to want to isolate V. In the case of multiplying, you are actually adding more M to the same side. I will demonstrate what it will look like.

`D=(M)/(V)` [multiply both sides by M]

`MD=(M^2)/(V)`

Now, you can multiply both sides by M, and still get the right answer, but that just takes more unnecessary steps. When you say "D=M/V so M/V*M cancels out M snd D*M is Dm=V", that is incorrect. M/V*M DOES NOT cancel out M. It create M² instead.

I hope this answered your question. Let me know if you have anymore questions in the comments.