Choose a representation
Carry units through density, area and consumption calculations. Squaring a length conversion squares its numerical factor. Inverse proportionality applies only when total work stays fixed.
Worked example
A material has density 2 grams per cubic centimeter. A solid sample has volume 2000 cubic centimeters. What is its mass in kilograms? Multiply density by volume to obtain grams. Divide grams by 1000 to convert to kilograms. Substitute the given numbers: 2 × 2000 ÷ 1000 = 4. The requested value is 4.
Contrast a wrong operation
In that example, 4000 follows this error: Stop in grams but label the result kilograms. The correct requested value is 4. Explain which quantity the mistaken method is actually calculating.
Connect a second form
4 equally productive workers complete a fixed job in 6 hours. At the same constant individual rate, how many hours would 8 workers need? Compute the fixed amount of work in worker-hours. Divide by the new worker count, assuming no change in productivity. Substitute the given numbers: 4 × 6 ÷ (8) = 3. The requested value is 3.
Transfer and check
A material has density 2 grams per cubic centimeter. A solid sample has volume 2500 cubic centimeters. What is its mass in kilograms? Pause before checking. Answer: 5. Multiply density by volume to obtain grams. Divide grams by 1000 to convert to kilograms. Substitute the given numbers: 2 × 2500 ÷ 1000 = 5.
Boundaries of the method
Square centimeters and centimeters need different conversion factors. Fuel per distance is the reciprocal of distance per fuel. More equally productive workers reduce time only under the fixed-work model. This lesson samples a PSAT/NMSQT objective; its examples are original and do not claim official question status or full coverage.
A material has density 2 grams per cubic centimeter. A solid sample has volume 2000 cubic centimeters. What is its mass in kilograms?
- Multiply density by volume to obtain grams.
- Divide grams by 1000 to convert to kilograms.
- Substitute the given numbers: 2 × 2000 ÷ 1000 = 4.
- The requested value is 4.
Compare the other answer choices
Divide volume by density instead of multiplying before unit conversion.
Use the density twice during conversion.
Stop in grams but label the result kilograms.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Math specifications