Find a Remainder Using Congruences: 3491/9

This video explains how to use a congruent to b modulo n to determine the remainder of a quotient.

[Ashmit-ovrw]

Thanks man, I had already studied the number theory but was stuck at its applications, I had my submit due today, you came in like a god’s helper in my life 😅🔥. Thank you. hope you have a nice day.

[devondevon]

Answer =8
3491 can be written as
3, 000 + 400 + 91
Since 9 divides 90, then
91 is congruent to 1 mod 9, then 1 can be replaced 91. In other words, when 91 is divided by 9, the remainder is 1; hence
3, 000 + 400 + 1
400 can be written as 4 x 100,
but 100 is congruent to 1 mod 9 since 9 divides 99
hence 400 is congruent to 4 mod 9; hence 4 can replace 400; hence
3000 + 4 + 1, the last step is 3000
since 9 divides 999 or 999 is congruent to 0 mod 9, then
1000 is congruent to 1 mod (9), hence 3000 (or 3 x 1000) is
congruent to 3 mod (9). Hence 3 can replace
3, 000, hence
3 + 4+ 1 = 8
hence 3491 is congruent to 8 mod 9
The remainder is 8 Answer

[perpetualstudio]

I thought you subtracted 0 from the left side and 90 from the right side, so why didn't you do the same for both 400 and 3000