16/64 = 1/4...How to Reduce Fractions the 'Easy Way'!

Totally Clueless sent me an email reminding me of some famous 'fractured fraction' examples like the one in the title. Can you think of a couple of other two-digit examples of the same type that 'reduce' this way? Note that 10/30 = 1/3 doesn't qualify (the digits have to 'cancel' diagonally!).

Here is TC's version:
Note that the product 16 x 4 can be obtained by deleting the '1' and the 'x'!

READER/STUDENT CHALLENGE

(a) Find the other two instances of this 'weird' multiplication. The two factors have to be of the same type as in the example, i.e., a 2-digit number by a 1-digit number and the tens' digit of the 2-digit number must be 1.

(b) Most would find the other instances by guess-test. Here's a more significant challenge. Verify algebraically that there are exactly three such solutions.

(c) Is this problem equivalent to the 'easy way' to reduce fractions mentioned in the title of this post? Why or why not?