Step by step
The question
Question: work out 45 mod 11.
45 mod 11
Mod 11 means: the remainder after dividing by 11.
It is always a whole number from 0 to 10.
mod 11 = the remainder after ÷ 11
always 0 to 10
1 Divide by 11
Divide 45 by 11: 11 goes 4 times, that is 44, and 1 is left over.
45 = 11 × 4 + 1
Careful!
4 is how many times 11 goes in.
Mod asks for what is left over: 1.
Careful: not 45 mod 11 = 4 ✗
2 On the clock
Think of a clock with 11 numbers, 0 to 10.
So 45 mod 11 = 1.
45 mod 11 = 1
3 Check
Multiply back: 11 times 4, plus 1, is 45.
11 × 4 + 1 = 44 + 1 = 45
And 1 is from 0 to 10.
Right!
0 ≤ 1 < 11
Let's look back.
First: divide by 11.
Then: on the clock.
Last: check.
Answer
45 mod 11 = 1