The mass of a certain liquid is 1{,}260 grams. The liquid has a uniform density of 1.4 grams per cubic...

1. TRANSLATE the problem information

• Given information:
  • Mass of liquid = 1,260 grams
  • Density = 1.4 grams per cubic centimeter
• What we need to find: Volume in cubic centimeters

2. TRANSLATE the relationship into mathematical form

• The density formula: \(\mathrm{Density = \frac{Mass}{Volume}}\)
• Since we know density and mass but need volume, rearrange to:
  \(\mathrm{Volume = \frac{Mass}{Density}}\)

3. SIMPLIFY by substituting the known values

• \(\mathrm{Volume = \frac{1,260}{1.4}}\)
• To make this division easier, multiply both numerator and denominator by 10:
  \(\mathrm{Volume = \frac{1,260 \times 10}{1.4 \times 10}}\)
  \(\mathrm{= \frac{12,600}{14}}\)

4. SIMPLIFY the division

• \(\mathrm{12,600 \div 14 = 900}\)

Answer: 900 cubic centimeters (Choice B)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the density formula and use \(\mathrm{Volume = Density \times Mass}\) instead of \(\mathrm{Volume = \frac{Mass}{Density}}\).

Using the incorrect formula: \(\mathrm{Volume = 1.4 \times 1,260 = 1,764}\)

This leads them to select Choice C (1764).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when dividing by the decimal 1.4, either by incorrectly placing the decimal point or making calculation mistakes.

Common miscalculations might yield results like 90 or 9,000, leading them to select Choice A (90) or Choice D (9000).

The Bottom Line:

This problem tests whether students can correctly apply the density formula and handle decimal division. The key insight is recognizing that to find volume when given mass and density, you divide mass by density, not multiply them together.