Word Problem With Unit Fractions


The use of unit factions is convenient for everyday applications where we need to divide a set of things among an unequal number (usually larger) of individuals.

For instance, suppose a group of eight friends wants to share three pies in equal portions, how can they accomplish that? A straightforward division would not solve this problem because 3 divides 8 equals 0.375, and the presence of decimals complicates things even more.

I think by representing a fraction like 3/8 as a sum of two unit fractions (ie. 1/4 + 1/8) makes this kind of sharing problem much simpler. We can now infer that each person will get a quarter of a pie and one half of another quarter of a pie. Since dividing by half (or into quarters, one-eighths, etc.) is practically easy to do, this method could be useful for many similar problems, including the inheritance problem posed on the blog.

If the man's inheritance is to be shared in 1/2, 1/3 and 1/12 parts among his children, then adding these unit fractions gives 11/12, which mean he would leave 11 horses for his children, with one receiving six, one receiving four, and the third receiving one horse. Thus, my interpretation is that the horse that died would not cause any conflicts among his children based on the original interpretation of the will since they would be given 11 horses in total in the first place.


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