Assume an exactly 640-acre standard section, with no survey adjustments. How many acres are in the S 1/2 of the NW 1/4?
Correct Answer
B) 80 acres
Nominal aliquot area=640 acres×1/4×1/2=80 acres. Common errors: stopping at the NW 1/4 gives 160 acres; taking half of the whole section gives 320 acres; treating the S 1/2 as a quarter gives 40 acres.
Why This Is the Correct Answer
Option B is correct because 640 acres x 1/4 = 160 acres for the NW 1/4, and half of that is 80 acres. The question stipulates an exact 640-acre section with no survey adjustments.
Why the Other Options Are Wrong
Option A: 40 acres
Option A, 40 acres, results from treating the S 1/2 as a quarter (640 / 4 / 4 = 40). The S 1/2 halves the quarter section: 640 x 1/4 x 1/2 = 80 acres.
Option C: 160 acres
Option C, 160 acres, stops at the NW 1/4 (640 / 4 = 160) without taking the S 1/2. The correct result is 160 x 1/2 = 80 acres.
Option D: 320 acres
Option D, 320 acres, takes half of the whole section (640 / 2 = 320) and ignores the NW 1/4. The correct result is 640 x 1/4 x 1/2 = 80 acres.
Multiply all the fractions
Multiply 640 by each fraction in the description; S 1/2 of NW 1/4 is 640 x 1/2 x 1/4.
How to use: Use this for any aliquot-part acreage question in a standard section.
Exam Tip
Count each fraction in the description and include each one in the multiplication.
Common Mistakes to Avoid
- -Stopping at the NW 1/4 and reporting 160 acres
- -Taking the S 1/2 of the whole section (320 acres) instead of the S 1/2 of the NW 1/4
- -Treating the S 1/2 as a quarter and getting 40 acres
- -Assuming actual sections contain exactly 640 acres without checking the survey
Concept Deep Dive
Analysis
This question tests calculating acreage from an aliquot-part legal description. Work from the end of the description backward: take the NW 1/4 of the 640-acre section, then the S 1/2 of that quarter.
Background Knowledge
In the rectangular survey system, a section is nominally one square mile, or 640 acres. Aliquot parts describe fractions of a section, and acreage is found by multiplying 640 by each fraction in the description.
Real-World Application
An appraiser receives a legal description reading S 1/2 of NW 1/4 of a section. The appraiser computes a nominal 80 acres and then checks the actual survey, since real sections may differ from 640 acres.
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