Proportion equivalence — solve for the missing term: 24 / 18 = ? / 6. Compute the exact value that balances the proportion.

Introduction / Context:
Proportions equate two ratios. Solving for a missing term often boils down to either cross-multiplication or simplifying the known ratio and scaling it to the comparable denominator (or numerator). This reinforces fraction manipulation skills.

Given Data / Assumptions:

• 24 / 18 = x / 6.
• All terms are positive real numbers; an integer solution is expected due to clean factors.
• Goal: find x.

Concept / Approach:
Two efficient routes exist. Route 1: Reduce 24 / 18 first. Route 2: Cross-multiply directly. Reducing first often clarifies the necessary scaling and helps check reasonableness instantly.

Step-by-Step Solution:
Simplify 24 / 18 by dividing numerator and denominator by 6: 24 / 18 = 4 / 3.Set 4 / 3 = x / 6.Cross-multiply: 4 * 6 = 3 * x ⇒ 24 = 3x.Solve: x = 24 / 3 = 8.

Verification / Alternative check:
Compute decimals: 24 / 18 = 1.333..., and x / 6 with x = 8 gives 8 / 6 = 1.333..., confirming equality.

Why Other Options Are Wrong:
12 or 10 do not keep the ratios equal; 9 yields 9/6 = 1.5, not 4/3.

Common Pitfalls:
Forgetting to reduce the left fraction; mixing up cross-multiplication; dividing by the wrong factor when simplifying 24/18.

Final Answer:
8