What fraction of a section is represented by SE 1/4 of SE 1/4 of SE 1/4?

What fraction of a section is represented by SE 1/4 of SE 1/4 of SE 1/4?

• A. 1/64
• B. 1/16
• C. 1/8
• D. 1/32

Answer: (A)

Dividing a section successively into quarters multiplies the fraction by 1/4 each time. Start with the whole section, take the Southeast quarter—that’s 1/4 of the section. Then take the Southeast quarter of that piece, which is another 1/4, giving 1/4 × 1/4 = 1/16. Do the same one more time for the Southeast quarter of that piece, resulting in 1/4 × 1/4 × 1/4 = 1/64 of the original section. For context, a full section is 640 acres, so 1/64 of a section is 10 acres. The other fractions would correspond to fewer successive quarterings (for example, 1/16 is two quarterings, 1/8 would be three-eighths of a section—not formed by successive SE quarters).

Dividing a section successively into quarters multiplies the fraction by 1/4 each time. Start with the whole section, take the Southeast quarter—that’s 1/4 of the section. Then take the Southeast quarter of that piece, which is another 1/4, giving 1/4 × 1/4 = 1/16. Do the same one more time for the Southeast quarter of that piece, resulting in 1/4 × 1/4 × 1/4 = 1/64 of the original section. For context, a full section is 640 acres, so 1/64 of a section is 10 acres. The other fractions would correspond to fewer successive quarterings (for example, 1/16 is two quarterings, 1/8 would be three-eighths of a section—not formed by successive SE quarters).