In the rectangular survey system, how many acres are contained in the NE 1/4 of the SW 1/4 of Section 16?
Correct Answer
A) 40 acres
A section contains 640 acres. The SW 1/4 = 640 ÷ 4 = 160 acres. The NE 1/4 of that = 160 ÷ 4 = 40 acres. When reading legal descriptions, work from right to left.
Why This Is the Correct Answer
Option A (40 acres) is correct because we start with Section 16 (640 acres), then take the SW 1/4 (640 ÷ 4 = 160 acres), and finally take the NE 1/4 of that SW 1/4 (160 ÷ 4 = 40 acres). Reading the legal description from right to left ensures proper calculation sequence. Each quarter division reduces the acreage by a factor of 4.
Why the Other Options Are Wrong
Option B: 80 acres
Option B (80 acres) is incorrect because it represents half of a quarter section, not a quarter of a quarter section. This would be the result if you only divided the SW 1/4 by 2 instead of by 4, or if you calculated a half-quarter instead of a quarter-quarter.
Option C: 160 acres
Option C (160 acres) is incorrect because this represents the entire SW 1/4 of the section, not the NE 1/4 of the SW 1/4. This error occurs when someone stops the calculation after the first division and fails to apply the second fractional division.
Option D: 20 acres
Option D (20 acres) is incorrect because this would represent 1/32 of a section, which would require three quarter divisions rather than two. This error might occur from over-calculating or misunderstanding the fractional breakdown of the legal description.
The 640-4-4 Rule
Remember '640 Start, Divide by 4 for each Quarter' - Start with 640 acres in a section, then divide by 4 for each fractional part in the legal description. Count the fractions from right to left: Section 16 (640) → SW 1/4 (÷4 = 160) → NE 1/4 of that (÷4 = 40).
How to use: When you see a legal description with fractions, count how many '1/4' divisions there are, start with 640, and divide by 4 that many times. Always read from right to left in the description.
Exam Tip
Always write down '640 acres' first, then work through each fractional division step by step from right to left in the legal description, dividing by 4 for each quarter mentioned.
Common Mistakes to Avoid
- -Reading the legal description from left to right instead of right to left
- -Forgetting to apply all fractional divisions in the description
- -Confusing quarter sections (160 acres) with quarter-quarter sections (40 acres)
Concept Deep Dive
Analysis
This question tests understanding of the rectangular survey system (also called the Public Land Survey System), specifically how to calculate acreage within fractional parts of a section. The key concept is that legal descriptions are read from right to left, and each division creates smaller parcels by dividing the previous area by 4. A standard section contains 640 acres, and when divided into quarters, each quarter contains 160 acres. Further subdivision of a quarter section into quarters results in 40-acre parcels.
Background Knowledge
The rectangular survey system divides land into 6-mile square townships, which are further divided into 36 one-mile square sections of 640 acres each. Legal descriptions using this system describe property by identifying fractional parts of sections, with each quarter section containing 160 acres and each quarter-quarter section containing 40 acres.
Real-World Application
Appraisers frequently encounter properties described using the rectangular survey system, especially in rural areas and western states. Accurate acreage calculation is essential for determining property boundaries, calculating price per acre, and ensuring proper comparable property analysis in appraisal reports.
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