How do you solve Modulo 7?

Question

Complete the multiplication table for modulo 7 is what I am supposed to do. I have no clue what Modulo 7 is. Can anyone clue me in. Then, it says List the reciprocals for 0,1,2,3,4,5,6 in modulo 7. How many reciprocals does each number have? You don't have to solve that for me, I just wrote it to give your more info.

Answer 1

Think of the calendar. When 7 days go by, we are
on the same day. Another way to think of the
modulo 7 system is to picture a 7 hour clock.
What happens when we multiply 2*4?
Well, we go from 0 to 4 and then from 4 to 1.
So 2*4 = 1 in this system.
Third way to think of it: Cast out 7's. Every time
you go past a multiple of 7 just divide by 7 and
keep the remainder.
So here's the part of the table for multiplying by 2:
0, 2, 4, 6, 1, 3, 5.
Can you complete the table from here?
Let me give you the row for multiplying by 3
to help you out. You carry on from here!
0,3, 6, 2, 5, 1, 4.
Reciprocals: 0 has no reciprocal.
The others are
1, 4, 5, 2, 3, 6.
Notice that each nonzero number has a unique
reciprocal.
Hope that helps a bit!