Easy multiplication by 11

There are a number of simple techniques that can be used when multiplying by certain numbers. They are very useful in their own right but can be even more useful when combined with other techniques where they can facilitate the solution of more difficult problems.

Multiplying by 11

To multiply any number by 11 do the following:
Working from right to left

1. Write the rightmost digit of the starting number down.
2. Add each pair of digits and write the results down, (carrying digits where necessary right to left).
3. Finally write down the left most digit (adding any final carry if necessary).

It's as simple as that, e.g.

• Multiply 712x11

${\displaystyle {\begin{matrix}&7&&1&&2\\&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow \\7&&8&&3&&2\end{matrix}}}$

712x11=7832

The reason for working from right to left instead of the more usual left to right is so any carries can be added in. e.g.

• Multiply 8738x11

${\displaystyle {\begin{matrix}&8&&7&&3&&8\\&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow &+&\swarrow \searrow \\9&\leftarrow _{1}&6&\leftarrow _{1}&1&\leftarrow _{1}&1&&8\end{matrix}}}$

8738x11=96118