How do you multiply?

A short film

Some questions:

• What are the main themes of the film?
• What places are mentionned?
• What is the link between this multiplication technique and computers?

Ethiopian multiplication

How?

1. Compute $13\times 24$ using Ethiopian multiplication.
2. Try with $53\times 32$.

Why?

Notice that the number $137$ means $1\times 10^2+3\times10^1+7\times10^0$, i.e. we decompose the number $137$ into powers of $10$.

• Long multiplication uses the decimal decomposition of a number, also called base 10.
• Ethiopian multiplication decomposes a number in powers of $2$, also called base 2.
  • Indeed, we use $25 = 16 + 8 + 1$.
  • Then $25\times 31$ can be written $16\times31+8\times31+1\times31$.
• Write $25 = 2\times 12+1 = 2\times (2\times 6) + 1 = \ldots = 16+8+1$

How to find the binary representation of a number?

• Play with the cards