Step by step
The question
Question: work out 9 mod 10.
9 mod 10
Mod 10 means: the remainder after dividing by 10.
It is always a whole number from 0 to 9.
mod 10 = the remainder after ÷ 10
always 0 to 9
1 Divide by 10
Divide 9 by 10: 10 goes 0 times, that is 0, and 9 is left over.
9 = 10 × 0 + 9
Careful!
0 is how many times 10 goes in.
Mod asks for what is left over: 9.
Careful: not 9 mod 10 = 0 ✗
2 On the clock
Think of a clock with 10 numbers, 0 to 9.
So 9 mod 10 = 9.
9 mod 10 = 9
3 Check
Multiply back: 10 times 0, plus 9, is 9.
10 × 0 + 9 = 0 + 9 = 9
And 9 is from 0 to 9.
Right!
0 ≤ 9 < 10
Let's look back.
First: divide by 10.
Then: on the clock.
Last: check.
Answer
9 mod 10 = 9