The equation d = m/V gives the density d of an object with mass m and volume V. Which is an equivalent equation solved for V: dm = V, m/d = V, d/m = V, or m - d = V?

Step-by-step solution

1. 1

   Get the target variable out of the denominator first. You cannot isolate $V$ while it sits underneath, so multiply both sides by $V$ (non-zero, since a real object has volume):

   $dV=m.$

2. 2

   Divide by the coefficient of V. That coefficient is $d$, so

   $V=\frac{m}{d}.$

   This matches the second option.

3. 3

   Check by substituting back. Putting $V=\tfrac{m}{d}$ into the original:

   $\frac{m}{V}=\frac{m}{m/d}=m\cdot\frac{d}{m}=d\ \checkmark$

4. 4

   Test with a concrete example. A block with $m=20\ \text{g}$ and $V=4\ \text{cm}^3$ has $d=5\ \text{g/cm}^3$. Then $\tfrac{m}{d}=\tfrac{20}{5}=4$, the correct volume, while $dm=100$ and $\tfrac{d}{m}=0.25$ are both wrong.

5. 5

   Rule out the distractors by units. $m$ is in grams and $d$ in $\text{g}/\text{cm}^3$, so $\tfrac{m}{d}$ has units $\text{g}\div\text{g}/\text{cm}^3=\text{cm}^3$ — a volume, as required. By contrast $dm$ carries $\text{g}^2/\text{cm}^3$ and $m-d$ subtracts unlike units, which is meaningless. Unit checking alone identifies the answer.