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

Find all the pairs of equivalent fractions 4 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

Find all the pairs of equivalent fractions 4 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

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?

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?

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?

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?

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?

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?

⋂ ⋂ ⋂ | | | ⋂ ⋂ ⋂ | | |

= 1/466 = 1/3 | | | 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). ⋂ ⋂ ⋂ | | | ⋂ ⋂ ⋂ | | | = 1/466 | | | = 1/3 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 ⋂ ⋂ ⋂ | | | | ⋂ ⋂ | ⋂ ⋂ | | ⋂ ⋂ | | |

= 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 | | | | | = 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. 3/4 3/8 3/16 15/16 8/15 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. © D Cavill

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

3/4 3/8 3/16 15/16 = 1/16+ 1/8 + 1/4+ 1/2 8/15 = 1/3+ 1/5 7/24 = 1/8+ 1/6 | | | | | | | | | | | | | | | | | | ⋂ | | | | | |