Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 3
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13The next natural thought would be to define modular addition as the following:
( + ) (mod ) =
(mod ) +
(mod )
For example: (7 + 6) (mod 5) = 7 (mod 5) + 6 (mod 5) = (2 + 1) (mod 5) = 3
Try this one: (19+28) (mod 5) =
19 (mod 5) + 28 (mod 5) = (4 + 3) (mod 5) = 7 (mod 5) = 2
As we see with this example, we can’t just calculate each number with respect to (mod )
and add them together, sometimes we are required to simplify the sum in with respect to
(mod ) after we sum them. So we define modular addition as:
( + ) (mod ) = [ (mod ) +
(mod )] (mod )
In general, we know we’ve simplified it as much as possible when the result is
less that .
Exercise 3: Calculate each of the following.
(a) 5 + 9 (mod 8) =
5 + 1 (mod 8) = 6
(b) 43 + 37 (mod 10) =
3 + 7 (mod 10) = 10 (mod 10) = 0
(c) 124 + 199 (mod 5) =
4 + 4 (mod 5) = 8 (mod 5) = 3
(d) 34 + 121 (mod 11) =
1 + 0 (mod 11) = 1
3.2
Modular Multiplication
Modular multiplication is very similar to modular addition. We define it as:
(
) (mod ) = [ (mod )
(mod )] (mod )
Exercise 4: Calculate each of the following.
(a) 5
9 (mod 8) =
5
1 (mod 8) = 5
(b) 7
15 (mod 7) =
0
1 (mod 9) = 0
(c) 5782
2579 (mod 10) =
2
9 (mod 10) = 18 (mod 10) = 8
(d) 603
123 (mod 60) =
3
3 (mod 60) = 9
(e) 16
25 (mod 12) =
4
1 (mod 12) = 4
(f) 34
122 (mod 11) =
1
1 (mod 11) = 1
3
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education