Kemetic Multiplication

[Yaw Agbede]

Multiplication
Beatrice Lumpkin

Shortcuts were needed, and multiplication is a shortcut for addition, just as addition is a shortcut for counting. With the Egyptian method, this principle is easy to understand. In fact, tables were not needed in Egyptian multiplication. To illustrate: “13 hekats of grain are taken 27 times. How many in all?”32

Although the problem was stated in concrete terms, as hekats of grain, the numbers were thought of abstractly. The commutative law was used because it was easier to multiply by 13 than by 27.
Start with one 27 and then continue to double, which can be done simply by adding the number to itself.

1___27
2___54
4___108
8___216

At this point the scribe would stop because the next step would give 16, and only 13 of the 27's were wanted. Now the partial products are added to get 13 x 27.

1*___27*
2____54
4*___108*
8*___216*
1+4+8=13 ___ 27+108+216=351

13 x 27=351


Students enjoy using Egyptian multiplication and it is a natural way to illustrate the distributive property:

13 x 27 = (1 + 4 + 8)(27) = (1)(27) + (4)(27) + (8)(27)

Our current method of multiplication, brought to Europe by Arabic-speaking Africans, makes a good check for the earlier Egyptian method. This type of exercise helps many pupils realize, for the first time, the reasons behind the modern method of multiplication.

There was one exception to the doubling, or duplication, process of multiplication. Often, multiplication by 10 would be done directly. Examples of direct multiplication are shown in problems 39 and 41 of the papyrus written by the scribe Ahmose. This papyrus is known as the [r]hind Mathematical Papyrus after the [s]cotsman who [stole] it. Problem 39 asks:
“Multiply 4 so as to get 50.”

1____4
\10__40
\2___8
\½__ 2
Total 12 1/2

In problem 41 by Ahmose, 64 is multiplied by 10 directly. With hieroglyphs this seems especially easy, because it would only require changing units to tens and tens to hundreds, as shown below. However, the Ahmose papyrus is written in hieratic, the fast script.
Ahmose Papyrus.jpg

[Obadele Kambon]

Mo! Wei bɛyɛ adeɛ papa ama Ama ɛberɛ a ɔsua nkontaabuo wɔ Mdw Ntr mu. Meda ase!!!

[Yaw Asare Aboagye]

Multiplication
Beatrice Lumpkin

Shortcuts were needed, and multiplication is a shortcut for addition, just as addition is a shortcut for counting. With the Egyptian method, this principle is easy to understand. In fact, tables were not needed in Egyptian multiplication. To illustrate: “13 hekats of grain are taken 27 times. How many in all?”32

Although the problem was stated in concrete terms, as hekats of grain, the numbers were thought of abstractly. The commutative law was used because it was easier to multiply by 13 than by 27.
Start with one 27 and then continue to double, which can be done simply by adding the number to itself.

1___27
2___54
4___108
8___216

At this point the scribe would stop because the next step would give 16, and only 13 of the 27's were wanted. Now the partial products are added to get 13 x 27.

1*___27*
2____54
4*___108*
8*___216*
1+4+8=13 ___ 27+108+216=351

13 x 27=351


Students enjoy using Egyptian multiplication and it is a natural way to illustrate the distributive property:

13 x 27 = (1 + 4 + 8)(27) = (1)(27) + (4)(27) + (8)(27)

Our current method of multiplication, brought to Europe by Arabic-speaking Africans, makes a good check for the earlier Egyptian method. This type of exercise helps many pupils realize, for the first time, the reasons behind the modern method of multiplication.

There was one exception to the doubling, or duplication, process of multiplication. Often, multiplication by 10 would be done directly. Examples of direct multiplication are shown in problems 39 and 41 of the papyrus written by the scribe Ahmose. This papyrus is known as the [r]hind Mathematical Papyrus after the [s]cotsman who [stole] it. Problem 39 asks:
“Multiply 4 so as to get 50.”

1____4
\10__40
\2___8
\½__ 2
Total 12 1/2

In problem 41 by Ahmose, 64 is multiplied by 10 directly. With hieroglyphs this seems especially easy, because it would only require changing units to tens and tens to hundreds, as shown below. However, the Ahmose papyrus is written in hieratic, the fast script.
Ahmose Papyrus.jpg

If I'm not mistaken, this is explained in greater detail in Nile Valley Civilizations by Dr. Ivan Van Sertima