Exchanging is when you are subtracting and you do not have enough ones, tens, hundreds, etc. to take away and you need to exchange for a new group of ten, hundred, etc. For example, if you subtract [katex] 27 - 18, [/katex] you start with [katex] 7 [/katex] ones and need to take away [katex] 8. [/katex] There are not enough, so you exchange one of the tens in [katex] 27 [/katex] for ones. Then you have [katex] 1 [/katex] ten and [katex] 17 [/katex] ones. Now you can subtract [katex] 8 [/katex] ones from [katex] 17 [/katex] ones, leaving [katex] 9 [/katex] ones.