An object has a mass of 168 grams and a volume of 24 cubic centimeters. What is the density, in...

1. TRANSLATE the problem information

• Given information:
  • Object mass = 168 grams
  • Object volume = 24 cubic centimeters
  • Need to find density in grams per cubic centimeter

• This is asking for density, which requires the density formula

2. TRANSLATE the mathematical relationship

• Density formula: \(\mathrm{Density = Mass ÷ Volume}\)
• Substitute the given values: \(\mathrm{Density = 168\text{ grams} ÷ 24\text{ cubic centimeters}}\)

3. SIMPLIFY the calculation

• \(\mathrm{Density = \frac{168}{24}\text{ grams per cubic centimeter}}\)
• \(\mathrm{168 ÷ 24 = 7}\)
• Therefore: \(\mathrm{Density = 7\text{ grams per cubic centimeter}}\)

Answer: A. 7

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students don't recall or correctly apply the density formula, using incorrect mathematical operations instead of division.

Instead of dividing mass by volume, they might:

• Add: \(\mathrm{168 + 24 = 192}\), leading them to select Choice C (192)
• Subtract: \(\mathrm{168 - 24 = 144}\), leading them to select Choice B (144)
• Multiply: \(\mathrm{168 × 24 = 4,032}\), leading them to select Choice D (4,032)

The Bottom Line:

This problem tests whether students can recall and correctly apply the fundamental density relationship. The arithmetic is straightforward once the correct formula is identified, but confusion about the density concept leads to using the wrong operation entirely.