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?

| | | ⋂ | | | | | ⋂ ⋂ |

| | | | | | | ⋂

| | | | | | | || | | || |

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?

| | | ⋂ | | | | | ⋂ ⋂ |

| | | | | | | ⋂

| | | | | | | || | | || |

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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