Egyptian Mathematics
By Edwin Barnes
7 Kolbe
St Joseph’s Catholic and Anglican
School
Egyptian Number Symbols
The Egyptians didn’t use numbers like we
do, they used symbols to represent the
numbers instead.
10000
100
000
000
=1
000
symbolsfor
reflect
everyday
one
may
come
The symbol
geta
ten
more
thousand
hundred
million
thousand
is
ais is
aa
Egyptian
things.
is a
fromcalled
alily.
finger.
Everyone
starts
complicated
water
finger.
thousand
god
Perhaps
It
isHeh.
shows
aas
frog,
the
itItThis
isalso
the
sometimes
numbers
a symbol
finger
leaf,
means
ten
coil
of
rope.
off
counting
on but
their
fingers!
geta
stem
thousand
as
just
bigger.
atadpole.
and
very
times
root,
large
The
symbol
as
number,
not
big
the
as
forlike
the
ten
is a piece
flower.
symbol
'squillion'.
forofone!
rope.
Numbers
In
thisthe
system
is better
To some
make aways,
number,
Egyptians
would than
write ours
because
if we want
to write
the number
one
down
the symbols
in order
of largest
to smallest
million,
have
seven
digitsFor
to write,
but the
from left we
to right
to form
groups.
example:
Egyptians only had to write one.
= 22
But the downside of the system
is that if they
wanted to
=write
7 the number one less than one
million, 999,999, they would have to write 9
one hundred thousands, 9 ten thousands and
so on down to 9 ones, using a massive
total
of
= 266
54 digits!
Addition
 The
of addition
was veryAddition.
simple
Thismethod
is an example
of Egyptian
 They collected together the symbols that
were the same from both of the numbers
 If there were ten of the same symbol, it
could then be substituted for the symbol
higher up in value
Subtraction
To subtract a number, the Egyptian would
write down the two numbers, and then
take away the symbols that appeared in
the second one from the first one.
For example:
Subtraction
 This is, however, complicated when more
of a symbol are to be taken away than
there are present, for example 63 - 48
 In this case, they would convert one of the
tens into ten units, and use it to complete
the calculation, for example:
Multiplication
And this column
They
drew
a
table
like
this:
 The Egyptians used quite a complex
is the number in
the firstwould
column find

The
Egyptians
method
of multiplication.
This
multiplied by 12
column is
the numbers in the first
the use the example of 12 x 17
 Weallwill
columnIt isthat
add up to 17,
POWERS
easy to complete these
OF TWO
which columns
is 1 + 16
because, as you
are only using powers of
 Then they
would
find
the
two, each
number
is the
number
above
it doubled
multiples
of 12
which
correspond, and add them
together like so:
Division
They
Division
in Ancient
required
would
draw theEgyptian
“powerstimes
of two”
table
the useagain,
of multiplication
and
often3 involved
but this time
using
They then
found the
fractions.
They would keep
corresponding
goingscribes
until 42 could
 This
is because the Egyptian
powers
of 2 and
made
in theto
right
added recognised
them
that division isbethe
inverse
together to find the
column
multiplication, and used that
fact to help
answer
them work out divisions
 They didn’t divide as we would, but asked
themselves a x ? = b (instead of a / b = ?)
 We can use the example 42 divided by 3.
Fractions
an example
of an
Egyptianused
Fraction
Here
Theisfractions
that the
Egyptians
were
not so different to ours, except that they were
This symbol represents
limited to the use of unit fractions,
which
are
a “part”. It is like
the
numerator, but always
fractions that have a numerator
of 1.
means
1
 The fractionsThis
they use do not have a
represents the fraction ½
numerator and a denominator, they are made
up of a number and then a “mouth” symbol
This is the denominator
on top of it.
Fractions
There are some rules about expressing fractions as
a sum in this way:
 If an Egyptian wanted to write a fraction
1. When a fraction can be expressed in more than
with
numerator
of more
than
one,the
such
one aform,
use the form
which
requires
least
as
¾, ⅔ of
orunit
⅜, then
they would have to
number
fractions.
it asthe
several
fractions
added
2. express
Always use
largest unit
unit fraction
possible
unless this
means
that the previous rule cannot
together.
For
example:
be complied with.
3. No unit fraction may be used more than once in
an expression, so you can’t write ⅔ as ⅓ + ⅓
4. Write the unit fractions in order of size from
largest to smallest.
The Eye of Horus
TheEach
Eye of
Horus
an iconic
part
of theisEye
represents a fraction
symbol often associated with
Ancient Egypt and its
mathematics.
Each fraction is half the one before it,
The name
from the
Egyptian
andcomes
the fractions
keep
going on,
God of mathematics,
getting smallerHorus.
and smaller
It represents the basis of Egyptian
The ideathe
is that,
if you go on forever
mathematicsunit fractions.
and then the
you ancient
add all the fractions
It also symbolizes
together,
eventually
you’ll get to 1
mathematical
concept
of infinity
The Eye of Horus
For example:
At this point, we reached a total of
8191/8192, or 0.9998779296875,
which is very, very close to 1, but not
quite there. The more fractions you
add on, the closer you get to 1, but
you will never actually reach 1 unless
you carry on to infinity
Units of Measurement
1 Palm used their own body to
The Egyptians
1 Digit
measure things around, which often meant
that measurements were not very accurate
or consistent
1 Cubit
Thank you for
watching my presentation
By Edwin Barnes
7 Kolbe
St Joseph’s Catholic and Anglican
School