A property in Township 3 North, Range 4 West, Section 15, NE 1/4, SW 1/4 contains how many acres?
Correct Answer
C) 40 acres
Why this is correct: A standard section is 640 acres. The description 'NE 1/4 of SW 1/4' means taking a quarter of a quarter. Calculate: 1/4 * 1/4 = 1/16 of the section. Acres = 640 acres / 16 = 40 acres. Why the other choices are wrong: 160 acres is the size of a quarter-section (640/4). 20 acres would be 1/32 of a section (e.g., a quarter of a quarter of a quarter). 10 acres is 1/64 of a section. Exam tip: Multiply the fractions: (1/4)*(1/4)=1/16. Then divide 640 by the denominator (16).
Why This Is the Correct Answer
Option C is correct because the calculation follows the proper PLSS subdivision method. The legal description 'NE 1/4, SW 1/4' means you take 1/4 of 1/4, which equals 1/16 of the total section. Since a section contains 640 acres, you divide 640 by 16 to get 40 acres. This represents the northeast quarter of the southwest quarter of Section 15.
Why the Other Options Are Wrong
Option A: 160 acres
160 acres would represent 1/4 of a section (640 ÷ 4 = 160), which would be described as simply 'SW 1/4' without the additional 'NE 1/4' subdivision.
Option B: 20 acres
20 acres would represent 1/32 of a section (640 ÷ 32 = 20), which is not the result of multiplying 1/4 × 1/4 = 1/16 as described in this legal description.
Option D: 10 acres
10 acres would represent 1/64 of a section (640 ÷ 64 = 10), which would require three subdivisions like NE 1/4 of NE 1/4 of SW 1/4, not the two subdivisions given in this legal description.
The 640 Division Rule
Remember 'Six-Forty Divide' - Start with 640 acres per section, then divide by the denominator you get when multiplying all the fractions in the legal description. For 1/4 × 1/4 = 1/16, divide 640 by 16.
How to use: When you see fractional legal descriptions, multiply all the fraction denominators (4 × 4 = 16), then divide 640 by that result (640 ÷ 16 = 40 acres).
Exam Tip
Always write out the fraction multiplication on your scratch paper: 1/4 × 1/4 = 1/16, then calculate 640 ÷ 16 = 40. Don't try to do this math in your head.
Common Mistakes to Avoid
- -Confusing the order of directional descriptions (reading SW 1/4, NE 1/4 instead of NE 1/4, SW 1/4)
- -Adding fractions instead of multiplying them (1/4 + 1/4 instead of 1/4 × 1/4)
- -Forgetting that each section contains exactly 640 acres regardless of township or range numbers
Concept Deep Dive
Analysis
This question tests understanding of the Public Land Survey System (PLSS), specifically how to calculate acreage within subdivided sections. The PLSS divides land into townships, ranges, and sections, with each section containing exactly 640 acres. When sections are subdivided using fractional descriptions like 'NE 1/4 of SW 1/4,' you must multiply the fractions to determine what portion of the total section is being described. This is fundamental knowledge for real estate appraisers who must accurately determine property sizes from legal descriptions.
Background Knowledge
The Public Land Survey System divides land into 6-mile square townships, which are further divided into 36 one-mile square sections of 640 acres each. Sections can be subdivided into quarters (160 acres), quarter-quarters (40 acres), and smaller parcels using fractional descriptions.
Real-World Application
Appraisers frequently encounter PLSS legal descriptions when valuing rural properties, farmland, and undeveloped parcels. Accurate acreage calculation is essential for determining property boundaries, calculating price per acre, and ensuring comparable sales are truly comparable in size.
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