Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 2
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Modular Operator
The modular operator might seem a little intimidating at first, but it’s really not. All it does
is, given 2 integers ( and ), it produces the remainder when the first number is divided by
the second.
Notation:
(mod ) =
This means that when
is divided by , there is a remainder of .
We say: “ modulo
is equal to ”.
Examples:
(a) 7 (mod 4) =
3
(b) 15 (mod 3) =
0
(c) 19 (mod 4) =
3
(d) 21 (mod 5) =
1
Exercise 2: Calculate each of the following.
(a) 7 (mod 5) =
2
(d) 17 (mod 8) =
1
(b) 8 (mod 4) =
0
(e) 37 (mod 6) =
1
(c) 8 (mod 3) =
2
(f) 124 (mod 60) =
4
3.1
Modular Addition
Modular addition is actually quite straight forward.
For example:
(1 + 2) (mod 4) = 3
(4 + 5) (mod 5) = 9 (mod 5) = 4
Pretty simple right? What if it got more complicated though, like this one?
(187468 + 847361) (mod 2) =
This is not an easy calculation, unless you have a calculator, but that defeats the purpose
of modular arithmetic, which is to simplify complicated calculations.
So, we propose an idea: What if we were to calculate each number with respect to that
modulo before we add them together? Now this complicated question becomes really simple:
(187468 + 847361) (mod 2) = (0 + 1) (mod 2) = 1
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