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So, while I was solving the examples I found a pattern between the mixed number and the dividing number.
For example :
7 & 1/5−6 and 7 & 1/5÷6
The mixed number (7 & 1/5) and the dividing number (6) shares a common point. So when the mixed number is converted into a improper fraction, the dividing number is a factor of the numerator of the improper fraction.

: 7 & 1/5 - 6 : 7 & 1/5 ÷ 6
= 36/5 - 30/5 = 36/5 * 1/6
= 6/5 = 6/5

As you can see 6 ( the dividing number ) is a factor of 36 ( the numerator of the improper fraction ).