1. Egyptian Fractions Learning Objective
To add fractions by using a common denominator

2. Find all the pairs of equivalent fractions4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
Find all the pairs of equivalent fractions

3. Find all the pairs of equivalent fractions4 10 1 2 3 4 16 32 20 40 9 12 1 3 16 28 6 9 9 81 50
125
1000
3000 2 5 2 3 4 7
3000
4000
Find all the pairs of equivalent fractions

4. Which fraction is the largest?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
Which fraction is the largest?

5. Which fraction is the largest?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
Which fraction is the largest?

6. Which fraction is the smallest?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
Which fraction is the smallest?

7. Which fraction is the smallest?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
Which fraction is the smallest?

8. How many fractions are bigger than half?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
How many fractions are bigger than half?

9. How many fractions are bigger than half?4 10 1 2 3 16 32 20 40 9 12 28 6 81 50
125
1000
3000 5 7
4000
How many fractions are bigger than half?

10. ⋂ ⋂ ⋂ | | | ⋂ ⋂ ⋂ | | |

11. = 1/466 = 1/3 | | | Egyptian Fractions
This is how the Egyptians wrote the numbers 1, 10 and 100
| = 1 ⋂ = = 100
 They only used fractions with a numerator of one - meaning 'One part in ...' (with the very rare exception of 2/3).
⋂ ⋂ ⋂ | | | ⋂ ⋂ ⋂ | | |
= 1/466
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= 1/3
Show how the Egyptians would have expressed the following fractions.
a) 1/4 b) 1/30 c) 1/45 d) 1/321

12. 1/ /30
1/ /321
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13. = 1/3+ 1/2 = 2/6 + 3/6 = 5/6 | | | | | = 1/4+ 1/10 = 5/20 + 2/20
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
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= 1/4+ 1/10
= 5/20 + 2/20
= 7/20
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14. | | | ⋂ ⋂ | | | | ⋂ | | | | | | | | | ⋂ | | | | | |
What fractions are shown below?
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Answers

15. Write these fractions like an Egyptian without repeating the same fraction more than once.
3/4 3/8 3/16
15/16 8/15 7/24
Now choose your own fractions and write them like an Egyptian.
Answers

16. © 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/ / / /776
This demonstrates the skill in which the Egyptians could manipulate unit fractions.
© D Cavill

17. 5/12 8/21 21/200 7/12 7/8 | | | ⋂ | | | | | ⋂ ⋂ | ⋂ | | | | | | |
What fractions are shown below?
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5/12
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8/21 ⋂
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21/200
7/12
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7/8

18. 3/4 3/8
3/ /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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