Ponit 5 and 6 can be simplified to the following non-formula approach

if x and y and two integer and they are divided by the same no. then you can multiply the remainder of two or more integers directly and then divide the product of the remainders by the divisor to get the reminder for the product of the integers.

e.g if x leaves a remainder 5 upon division by 9 and y leaves a reminder 7 upon division by 9 then x will leave the remainder 7*5/9 (multiply the reminders and then divide by 9). which is 8

similarly

remainders can be added and subtracted directly if the divisor of two or more integers is the same.

e.g

if x leaves a remainder 5 on division by 8 and y leaves a remainder 6 on division by 8 then X-Y will leave remainder 5-6/8=-1/8 will leave a remainder of 7. simply subtract the remainders and then divide by the divisor.