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EGYPTIAN MULTIPLICATION

The Ancient Egyptian used pencil and papermethod for multiplication which was based ondoubling and addition.

Unique method which they correctly viewed asrepeated addition.

Based on doubling and is also known as the

didactic method.

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Starting with one and doubling, they obtained a never-

ending sequence of numbers: 1, 2, 4, 8, 16, 32, 64,

128

These numbers are the powers of two: 20, 21, 22, 23, 24,

25, 26, 27,

Egyptians figured out is that any integer can be written

as a sum of the powers of two without repeating anyof them

For example,

14 = 8 + 4 + 223 = 16 + 4 + 2 + 1

45 = 32 + 8 + 4 + 1

160 = 128 + 32

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EGYPTIAN MULTIPLICATION OF22 x 65

Suppose we want to

multiply 22 x 65. 1 65

2 130

4 260

8 520

16 1040

Write 1 and 65,

meaning 1 lots of 65

Work down, doubling

both numbers until

the left side gets asclose as possible to,

but not larger than

22.

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1 65

2 130

4 260

8 520

16 1040

Add up the remaining

numbers on the rightto get the final

answer.

Cross out the other

rows of numbers.

Look for the numbers

on the left that addup to 22 (16+4+2).

1430

+

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EGYPTIAN MULTIPLICATIONOF 43 x 78

Suppose we want to

multiply 43 x 78. 1 78

2 156

4 312

8 624

16 1248

Write 1 and 78,

meaning 1 lots of 78

Work down, doubling

both numbers until

the left side gets asclose as possible to,

but not larger than

22.

32 2496

64 4992

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Add up the remaining

numbers on the rightto get the final

answer.

Cross out the other

rows of numbers.

Look for the numbers

on the left that addup to 43 (32+8+2+1).

1 78

2 156

4 3128 624

16 1248

32 2496

3354

+

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1 78

2 156

8 624

32 2496

3354

+

4 3

X 7 8

3 4 4

3 0 1

3 3 5 4

EGYPTIAN MULTIPLICATION

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1. If Ms. Nelly has to give 18 lectures in aweek, how many lecture she has to give in a

year?

2. An athlete jogs 26km in a day, how far willhe jog in 66 days?

3. A potter makes 45 pots in a week, how many

will he make in one and half year?

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1. If Ms. Nelly has to give 18 lectures in a week, how

many lecture she has to give in a year?

1 52

2 104

4 208

8 416

16 832

988

988 lectures in a year.

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2. An athlete jogs 26km in a day, how far will

he jog in 66 days?

1 66

2 132

4 264

8 528

16 1056

1716

1716 km in 66 days

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3. A potter makes 45 pots in a week, how many

will he make in one and half year?

1 78

2 156

4 312

8 624

16 1248

3510

One and half year = 52 weeks + (52 2) weeks= 52 weeks + 26 weeks= 78 weeks

3510 pots in one and half year.

32 2496

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