Post on 03-Jan-2016
transcript
Learning Objective
To add fractions by using a common denominator
Egyptian Fractions
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Find all the pairs of equivalent fractions
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Find all the pairs of equivalent fractions
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Which fraction is the largest?
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Which fraction is the largest?
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Which fraction is the smallest?
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
Which fraction is the smallest?
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
How many fractions are bigger than half?
410
12
34
1632
2040
912
13
1628
69
981
50125
10003000
25
23
47
30004000
How many fractions are bigger than half?
⋂ ⋂ ⋂ | | |⋂ ⋂ ⋂ | | |
Egyptian Fractions
This is how the Egyptians wrote the numbers 1, 10 and 100
| = 1 ⋂ = 10 = 100
They only used fractions with a numerator of one - meaning 'One part in ...' (with the very rare exception of 2/3).
| | |= 1/3
⋂ ⋂ ⋂ | | |⋂ ⋂ ⋂ | | | = 1/466
Show how the Egyptians would have expressed the following fractions.
a) 1/4 b) 1/30 c) 1/45 d) 1/321
1/4 1/30
1/45 1/321
| | | |
⋂ ⋂ | |⋂ ⋂ | | |
⋂ ⋂ ⋂
⋂ ⋂ |
To make more complex fractions like 5/6, the Egyptians added
different unit fractions together.
| | | | |
= 1/3+ 1/2
= 2/6 + 3/6
= 5/6
| | | | ⋂
= 1/4+ 1/10
= 5/20 + 2/20
= 7/20
What fractions are shown below?
| | | ⋂ | | | | | ⋂ ⋂ |
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Answers
Write these fractions like an Egyptian without repeating the same fraction more than once.
3/43/8
3/16
15/168/15
7/24
Now choose your own fractions and write them like an Egyptian. Answers
© D Cavill
Work like an Egyptian
Relatively little evidence of the mathematics of the Egyptians has survived due to the delicate nature of the papyrus, on which the work was written. However, a handful of papyri did survive, the largest and best preserved of these is the Rhind (also known as Ahmes) papyrus, now in the British Museum. This work was copied in 1650 BC by a scribe called Ahmes (or Ahmose) from a text written two or three centuries earlier and acquired by a British collector (Rhind) in 1858 AD. Here is a problem given on the Rhind Papyrus
Problem 31
A quantity, its 2/3, its ½ and its 1/7, added together become 33. What is the quantity?
The answer given is 14 ¼ + 1/56 + 1/97 + 1/194 + 1/388 + 1/679 + 1/776
This demonstrates the skill in which the Egyptians could manipulate unit fractions.
What fractions are shown below?
| | | ⋂ | | | | | ⋂ ⋂ |
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5/12 8/21
7/1221/200
7/8
3/43/8
3/1615/16 = 1/16+ 1/8 + 1/4+ 1/2
8/15 = 1/3+ 1/5 7/24 = 1/8+ 1/6
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