## 'Doing and Undoing' printed from http://nrich.maths.org/

Maybe you are used to making knots and sometimes you undo them!

Let's look at undoing some maths that's been done.

Suppose we have a starting number and then we doubled it.
That's the bit we'll call "doing".
To "undo" the maths we start with just the answer and see if we can get back to our starting number.
When I  doubled my starting number, I got $6$. What do I have to do, to "undo" the $6$ and get back to my starting number?
Suppose that I did it again with a new starting number so I doubled and got to $16$. What would you have to do to "undo" and get back to my new starting number?

Can you think what you would have to do to "undo" these three children's maths?

Danesh says
"I took $4$ away, what should I do to get back to my starting number?"
Meg says
" I added $8$, what should I do to get back to my starting number?"
Chris says
"I halved, what should I do to get back to my starting number?"

Now, if they all finished with a $12$ what were their starting numbers?

Photograph acknowledgements;

http://www.instructables.com/image/FPRA3T8FZ8J4A39/How-to-tie-various
-knots.jpg
http://2.bp.blogspot.com/-Jg0te1K_F5g/TpFcEY8xT6I/AAAAAAAAHy4/vgkke
-0QQ98/s1600/knot.jpg
http://www.instructables.com/image/F0PMDJ8FZ8J4A36/Figure-8-Knot.jpg