A metal sample has a density of 8 grams per cubic centimeter. What is the mass, in grams, of a 25 cubic centimeter sample of this metal?

Density is mass divided by volume, so mass equals density times volume. Multiply: $8 \frac{\text{g}}{\text{cm}^3} \times 25 \text{ cm}^3 = 200$ grams. The cubic centimeters cancel, leaving grams. A common wrong answer is $\frac{25}{8} = 3.125$, which comes from dividing volume by density instead of multiplying, which would give units of cubic centimeters squared per gram, which makes no sense. Another is 33, from adding $8 + 25$. Check units: they must come out in grams. Rearranging the density formula correctly is the key step.