That multiplication part is actually a way of checking
your answer by using the opposite operation. Confused? Okay, let's start with something more basic: subtraction and its opposite, addition.
Imagine that you don't have a calculator on hand to figure out the difference between two numbers. Pull out your pencil and some paper to do some quick math and then check it to see if you subtracted correctly.
For example, take this equation: 195927 – 6793 = x
and write it like this:
195927 - 6793 ------- 189134
Check your math! To do this, draw another line under the answer, 189134.
It should look like this:
195927 - 6793 ------- 189134 -------
Now, add the two bottom numbers (6793 + 189134) by writing your answer underneath the line you just drew . . .
. . . and it should look like this:
195927 - 6793 ------- 189134 ------- 195927
What do you get? 195927! The very top number and the very bottom number are the same. (If they aren't the same, then you need to redo the subtraction and check it again.)
You can use the same concept to check division. (What's the opposite operator of a division sign? Yep, a multiplication sign!)
So let's go back to your original question:
9 -- = 1 9
Check your math! Take the denominator (the bottom number of a fraction) and multiply it by the answer (which in this case is 1).
The equation looks like this:
9 x 1 = 9
1 x 9 = 9 (Look familiar?)
Here's another example: 731/17=43
731 ---- = 43 17
Check your math! 17 x 43 = 731
Get it? Got it? Good!