Step by step
The question
Question: work out (55 + 66) mod 9.
(55 + 66) mod 9
Mod 9 means: the remainder after dividing by 9.
mod 9 = the remainder after ÷ 9
1 Each remainder
Divide 55 by 9: 9 goes 6 times, that is 54, and 1 is left over.
55 = 9 × 6 + 1
66 is 9 × 7, plus 3.
66 = 9 × 7 + 3
Only the remainders matter: the groups of 9 can never change what is left over.
the 9s do not change the remainder
Careful!
Every number is swapped for its remainder, not just the first one.
Careful: not 1 + 66 ✗
2 Add the remainders
So we only need 1 + 3.
(55 + 66) mod 9 = (1 + 3) mod 9
1 plus 3 is 4.
= 4 mod 9
4 is already from 0 to 8.
= 4
3 Check
With a calculator: 55 plus 66 is 121.
That is 9 times 13, plus 4.
The same.
Right!
55 + 66 = 121 = 9 × 13 + 4
Let's look back.
First: each remainder.
Then: add the remainders.
Last: check.
Answer
= 4