For a standard-section acreage problem, start with 640 acres and multiply by each stated fraction. But do not stop at the arithmetic. Two descriptions can produce the same number while pointing to different land, and two parcels can overlap. A quick sketch catches mistakes a calculator cannot.
This worksheet builds on our Chapter 11 legal-descriptions guide. The examples are invented for study, not actual state-exam questions or descriptions to use in a transaction. Assume regular 640-acre sections and the exact dimensions stated in each exercise.
Check the starting point before multiplying
Look for three things: the area of the whole, the requested unit, and whether the description identifies a smaller part of one parcel or combines separate pieces. Write those facts above your calculation. If the question asks for land remaining after a sale, finding the area sold is only an intermediate step.
The Bureau of Land Management's explanation of legal descriptions describes the section system and the order of its subdivisions. NIST's conversion table gives 43,560 square feet per acre. We use those relationships below; the particular numbers and exercises are our own.
Problem 1: Follow the description into the section
Find the acreage: the west half of the northeast quarter of the southeast quarter of a standard section.
- Locate the southeast quarter first: 640 x 1/4 = 160 acres.
- Within that quarter, locate its northeast quarter: 160 x 1/4 = 40 acres.
- Take the west half of that smaller piece: 40 x 1/2 = 20 acres.
The single calculation is 640 x 1/4 x 1/4 x 1/2. To draw the parcel, work from the larger area toward the smaller one. Written descriptions put the smaller subdivision first, so drawing this example starts at the right-hand end of the fractional description.
Check: half of a 40-acre piece must be less than 40 acres. An answer of 80 means at least one subdivision was missed.
Problem 2: Same acreage, different location
Compare: the northeast quarter of the southwest quarter, and the southwest quarter of the northeast quarter, both in the same standard section.
Each calculation is 640 x 1/4 x 1/4 = 40 acres. They are not the same parcel. The first lies within the section's southwest quarter; the second lies within its northeast quarter. Mark the outer quarter on your sketch before dividing it again.
The multiplication can be rearranged without changing the answer. The directional words cannot be rearranged without changing the description. This is why matching acreage alone does not establish that two descriptions identify the same land.
Problem 3: Do not add the same ground twice
Find the combined area: Parcel A is the north half of the northeast quarter. Parcel B is the northeast quarter of that same northeast quarter. Both refer to the same standard section, and the question asks for the total distinct land covered.
Parcel A contains 640 x 1/4 x 1/2 = 80 acres. Parcel B contains 640 x 1/4 x 1/4 = 40 acres. However, all of B lies inside A. The combined area is therefore 80 acres, not 120.
You can check it as 80 + 40 - 40 acres of overlap = 80. Our existing discussion about AND in an acreage problem covers combining pieces. The extra check here is whether those pieces overlap.
Problem 4: Subtract after converting the units
Find the land remaining: a hypothetical owner starts with the 20-acre parcel from Problem 1 and sells one rectangular piece measuring 220 feet by 396 feet. The rectangle lies entirely inside the parcel. How many acres remain?
- Rectangle area: 220 x 396 = 87,120 square feet.
- Convert the area sold: 87,120 / 43,560 = 2 acres.
- Subtract from the original holding: 20 - 2 = 18 acres remaining.
Do not subtract 87,120 directly from 20. One figure is square feet and the other is acres. Also, 220 + 396 is not an area calculation. Multiplying two lengths gives square feet; adding lengths does not.
Know when the classroom assumption ends
BLM describes sections as usually 640 acres, not a promise that every actual surveyed section has exactly that area. Do not replace recorded survey information with the standard-section assumption used here. The arithmetic exercises do not resolve boundaries, ownership or a real conveyance.
For another check, explain each answer without looking at the calculation: 20 acres after three subdivisions; 40 acres each, but different locations; 80 distinct acres after removing overlap; and 18 acres left after a two-acre sale.
Continue with the Chapter 11 practice questions. For percentages, loan-to-value and closing calculations, use our four real estate math examples. You can also start the free course; certificate pricing is explained separately.
