Share as an Egyptian

Share as an Egyptian

The Egyptians were great mathematicians. They solved all kinds of problems using calculations such as marking the boundaries of the land when the Nile overflowed, the construction of pyramids, trade, distribution, etc. They knew the natural numbers and they used fractions with numerator 1, the unit fractions.An Egyptian fraction is a unit fraction and any fraction is a sum of different unit fractions.

For example the fraction 11 16it is written as the sum of the following unit fractions:

Egyptian fractions were used, among other things, to solve problems of equitable distribution. In the Rhind papyrus, which dates back to 1650 BC, the following problem was found: Share 6 breads among 10 men.

Activity 1:Write 27/32 as a sum of Egyptian fractions

Divisors of 32: 1, 2, 4, 8, 16, 32

2732

1 + 2 + 8 + 16 = 27

Divisors of 32: 1, 2, 4, 8, 16, 32

2732

1632

832

232

132

1 + 2 + 8 + 16 = 27

Divisors of 32: 1, 2, 4, 8, 16, 32

2732

12

14

116

132

2732

Activity 2:Share 6 chocolate bars between 8 friends

6 bars8 friends

68

6 bars8 friends

Divisors of 8: 1, 2, 4, 8

68

6 bars8 friends

2 + 4 = 6

Divisors of 8: 1, 2, 4, 8

68

2 + 4 = 6

Divisors of 8: 1, 2, 4, 8

68

48

28

Half a bar and one quarter for each friend

12

14

68

48

28

Activity 3:Distribute 10 sacks of rice among 16 people

10 sacks16 people

1016

10 sacks16 people

Divisors of 16: 1, 2, 4, 8, 16

1016

10 sacks16 people

2 + 8 = 10

Divisors of 16: 1, 2, 4, 8, 16

1016

2 + 4 = 6

Divisors of 8: 1, 2, 4, 8

1016

816

216

Half a sack and one eighth for each one

12

18

1016

816

216