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Egyptian Fraction PDF

The ancient Egyptians represented fractions as the sum of distinct unit fractions, where each unit fraction has 1 as the numerator and a different positive integer as the denominator. For example, they would write 5/8 as 1/2 + 1/8. To do this, they would find numbers that multiply the denominator, then choose the appropriate multipliers to equal the numerator. So for 5/8, the multipliers of 8 are 1, 2, 4, 8, and 2 + 8 = 10 = 5/8. They wrote fractions this way because their notation did not allow writing fractions like 2/5 directly. Representing fractions as sums of unit fractions was an extension of their division process.

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275 views2 pages

Egyptian Fraction PDF

The ancient Egyptians represented fractions as the sum of distinct unit fractions, where each unit fraction has 1 as the numerator and a different positive integer as the denominator. For example, they would write 5/8 as 1/2 + 1/8. To do this, they would find numbers that multiply the denominator, then choose the appropriate multipliers to equal the numerator. So for 5/8, the multipliers of 8 are 1, 2, 4, 8, and 2 + 8 = 10 = 5/8. They wrote fractions this way because their notation did not allow writing fractions like 2/5 directly. Representing fractions as sums of unit fractions was an extension of their division process.

Uploaded by

Frences Mae Turno Ebalo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SUBJECT: History of Mathematics TOPIC: Arithmetic in the Ancient World

REPORTER: Barrera, Melmarie D. SUBTOPIC: Egyptian Fraction


COURSE AND YR: BSE-Math 1 INSTRUCTOR: Ms. Myra Leonor Mon

EGYPTIAN FRACTION

An Egyptian fraction is a sum of positive (usually) distinct unit fraction. The famous RHIND
PAPYRUS dated to around 1650 BC contains a table of representation of as Egyptian fraction.

➢ The Egyptians of 3000 BC had an interesting way to represent fractions. Although they had a
notation for ½, 1/3, ¼ and so on (these are called reciprocals or unit fractions, since they are 1/n for
some number n) their notation did not allow to write 2/5, ¾, 4/4, 5/7 etc. They were able to write any
fraction as a sum of unit fractions were different.

EXAMPLE:

𝟓 𝟏 𝟏
𝟏. = +
𝟖 𝟐 𝟖

How to solve? (TRIAL AND ERROR)

Note: The given example we can possibly multiply it by (2/2, 3/3,4/4,5/5 and so on.). It depends
on the given example.

5/(8 ) (2/2)= 10/16 (1*16), (2*8), (4*4), (8*2), (16*1)

o Find the numbers that multiplies of the denominator:


Result (1,2,4,8,16)
o After of finding the number that multiplies of denominator.
Get the total of numerator in the result in multiplies of denominator.
(2+8=10)

Therefore:

2/16 + 8/(16. ) = (10 )/(16 )

Recheck:

2/16+8/16= (2+8)/16 = 10/16 reduce it by the lowest term 1/8+1/2=10/16

o After of rechecking of the result, finalize your answer by sequencing it from least to greatest
denominator.
ANSWER: 5/8= 1/2+1/8

➢ A fraction written as a sum or distinct unit fractions is called an Egyptian Fraction.

Rules in Egyptians Fractions or Unit Fractions


❖ A unit fraction is a rational number that can be written as a fraction where the numerator is one and
the denominator is a positive integer.
❖ A unit fraction is reciprocal of a positive integer, 1/n. Examples are 1/2, 1/3, 1/4 ,1/5, etc.
❖ 1/1 = is an improper unit fraction.
❖ 1/2, 1/3,1/4, 1/5, etc.… … is a proper unit fraction
❖ A unit fraction is a fraction with 1 in the numerator, such as ½ or ¼.
❖ They would write ¾ as ½ + ¼.
❖ They would not write ¾ as ¼ + ¼ + ¼ because these addends are not distinct, so all of the
denominators are need to be different but all of the numerators need to be equal to 1.
❖ Writing a fraction as the sum of distinct unit fractions was a natural extension that came from a
process for dividing.
❖ It is also useful for comparing fractions and order them from least to greatest (or vice versa).

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