Fraction Tasks
1. Divide nine loaves of bread equally between ten people.
Two Forms of Division
(a) Nine-tenths, one-tenth.
(b) Two thirds, one-fifth, one-thirtieth; one-half, one-fifth, one-fifth.
Egyptian fractions were either unit:
a one in the numerator;
or two-thirds.
Break many loaves into two-thirds, one-third segments.
Use these facts:
1.a two-thirds (likewise two thirds), one-fifth, and one-thirtieth sum to nine-tenths;
1.b one-half, one-fifth, and one-fifth also sum to nine-tenths;
1.c to see both 1.a and 1.b convert all fractions to thirtieths and add,
finding the two total to twenty-seven thirtieths.
All ten receive comparable sized chunks of bread, under the second (older, Egyptian) form of division.
The modern method yields the first division.
Nine people receive large pieces. One person gets nine small items.
6 6 2000 Version http://www.cs.ucla.edu/~klinger/etext.html