Assume a section contains exactly 640 acres. How many acres are in its NW 1/4 of the SE 1/4?
Correct Answer
B) 40 acres
640 acres × 1/4 × 1/4 = 40 acres. Common errors: stopping at the SE 1/4 gives 160 acres; dividing by 4 one time too many gives 10 acres; treating the NW 1/4 as a half gives 80 acres.
Why This Is the Correct Answer
Option B is correct because the NW 1/4 of the SE 1/4 is one quarter of one quarter of the section. The calculation is 640 acres x 1/4 x 1/4 = 40 acres. Each quarter step divides the previous area by 4.
Why the Other Options Are Wrong
Option A: 10 acres
Option A, 10 acres, comes from dividing by 4 one time too many: 640 / 4 / 4 / 4 = 10. The description has only two quarter steps, so the correct result is 640 x 1/4 x 1/4 = 40 acres.
Option C: 80 acres
Option C, 80 acres, comes from treating the NW 1/4 as a half: 640 / 2 / 4 = 80. Both parts are quarters, so the correct result is 640 x 1/4 x 1/4 = 40 acres.
Option D: 160 acres
Option D, 160 acres, comes from stopping at the SE 1/4: 640 / 4 = 160. The description then takes the NW 1/4 of that quarter, so 160 / 4 = 40 acres.
Read right, divide each step
Start from the last fraction and work left, dividing 640 by each denominator. Two quarters means divide by 4 twice.
How to use: Use this method on any aliquot part question in the rectangular survey system.
Exam Tip
Count the fractions in the description and divide once for each. Distractors often come from one too few or one too many divisions.
Common Mistakes to Avoid
- -Stopping after the first quarter division
- -Dividing by 4 more times than the description calls for
- -Treating a quarter as a half
Concept Deep Dive
Analysis
This question tests aliquot part calculations in the rectangular survey system. Read the description from right to left, multiplying the section's acreage by each fraction. With 640 acres, one quarter of a quarter yields 40 acres.
Background Knowledge
In the rectangular survey system, each township is divided into 36 sections of approximately one square mile, or 640 acres, each. Sections are divided into aliquot parts such as halves and quarters. Actual sections can vary from 640 acres, which is why questions often state the assumption.
Real-World Application
An appraiser receives a rural assignment described as the NW 1/4 of the SE 1/4 of a section. She computes a nominal 40 acres and then checks the survey or tax records for the actual acreage, since real sections can vary.
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