About the Fraction Five Divided-By Eight

On 1 February 2007, Math Reading Group at SCC watched a Discovery Channel video clip about fractions. The video clip used a fraction having five as the numerator and eight as the denominator.


The fraction was used to demonstrate the problem of an ancient tribe having to equally share five loaves of bread between eight people.

   let 'B' be a loaf of bread and 'P' is a person

   B B B B B 
   P P P P P P P P
   not every 'P' can have a 'B'

   divide each 'B' into two equal halves forming ten 'b'
   each 'b' is 1/2 of a 'B'

   b b b b b b b b b b 
   P P P P P P P P

   each 'P' gets one 'b' with two 'b' leftover

   b b
   P P P P P P P P

   divide each 'b' into 4 equally sized pieces forming 8 'e'

   each 'e' is 1/8 of a 'B'

   e e e e e e e e
   P P P P P P P P

   each 'P' gets one 'e' with zero 'e' leftover

   therefore, each 'P' gets 1/2 + 1/8 of a 'B'

Fractions must have a common denominator when added together. 1/2 and 4/8 are equivalent fractions because 1 divided-by 2 equals 4 divided-by 8.

    1     1     4     1     5
   --- + --- = --- + --- = ---
    2     8     8     8     8

Decimal numbers (i.e. numbers with decimal points; floating-point; real) and percents. Each 'P' received 5/8 of 'B'. The fraction can be morphed into a decimal number and a percentage.

   5 / 8 = 0.625

   0.625 x 100% = 62.5%

   each 'P' got to eat 62.5% of all the 'B'

Creator: Gerald D. Thurman [gthurman@gmail.com]
Created: 02 February 2007

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