**Ancient Egyptian Mathematics**

Addition and Subtraction

Numerical Characters

1

10

100

1,000

10,000

100,000

1,000,000

Reading Numbers

Lower numbers are written in front of higher numbers

Start at the top when there is more than one row of numbers

These processes simply required counting glyphs much like our base ten system

You simply collect all symbols of a single type and replace any ten of those symbols with a symbol of the next higher order

and

is equal to

Multiplication and Division

**The Basics**

is 12,204

is 1,100,020

**Applying This System**

Modern Applications

12x12=48+96=144

12 = 1100 in base 2

**Modern Applications**

Computers multiply and divide the same way Egyptians did!!

Humans operate in base 10. Computers operate in base 2, they only know the symbols 0 and 1.

1, 2, 3, 4 = 1, 10, 11, 100

Multiplying by 2 in binary is easy.

Add 0 on end like x10 in base 10.

1 = 1

2 = 10

4 = 100

8 = 1000

24 = 1 1000

48 = 11 0000

96 = 110 0000

1100 x 1100 = 1 1 0000

+ 1 1 0 0000

-------------

1001 0000

Background Information

The Rhind Papyrus

dates from approximately 1650 B.C.E.

It remains one of the best sources of ancient Egyptian maths

The papyrus lists the practical problems encountered in administrative and building works

contains arithmetic, algebraic, geometric and fraction problems

A Base-10 System

Ancient Egyptian mathematics use a

base 10 system

similar to our current mathematical system.

However, their characters, or glyphs, were represented by images, not numerals.

What did the Egyptians use Math for?

Measuring time

Measuring straight lines

Calculating level of Nile floodings calculating areas of land

Counting money, taxes

figuring out the numbers of days in the year (And they came quite close!)

This might seem complicated but we've seen it before

Multiplication and division use the counting glyphs.

To multiply two numbers, you need to understand

the double or the half of the integer.

1 35

2 70

4 140

8 280

(x2)

Let's Try - What is 35 times 11?

We will double 35 and 1

at the same time

until the multiples of 1 reach 11

1+2+8 = 11

35+70+280 = 385

Now Let's Replace the Integers with Glyphs!

Let's Try 35 times 11

(x2)

(x2)

(x2)

(x2)

(x2)

35 times 11 = 385

1

2

4

8

or

35

70

140

280

or

11

385

god with arms raised

lotus

finger

tadpole or frog

single stroke

cow hobble

coiled rope

One More Time

12 times 24 = 288

1 24

2 48

4* 96*

8* 192*

4 + 8 = 12

96 + 192 =

It works!

288

Addition and subtraction were a process of

grouping and regrouping.

Fractions

They used fractions like 1/2 and 1/4

but to make fractions like 3/4, they added pieces

3/4 = 1/2 + 1/4

Egyptians used fractions by adding pieces

For example, to write 2/5, they wrote 1/3 + 1/15

Written record of Egyptian factions goes back to the Rhind Papyrus

never

They repeated the same fraction twice when adding

The Ancient Egyptians used a number system based on

unit fractions

They used fractions of the form 1/n

Any other fraction had to be represented by

a sum of such fractions

(or reciprocals)

A fraction written as a sum of distinct unit fractions is called an

Egyptian Fraction

**by Becca Chang and Laura Micetich**