Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 8
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Problem Set
1. Calculate each of the following
(a) 100 (mod 3) =
1
(b) 451 (mod 5) =
1
(c) 490 (mod 7) =
0
(d) 234 (mod 4) =
2
(e) 478 (mod 6) =
4
(f) 582 (mod 9) =
540 (mod 9) + 42 (mod 9) = 6
(g) 679 (mod 8) =
640 (mod 8) + 39 (mod 8) = 7
(h) 12 + 18 (mod 9) =
4
(i) 73 + 58 (mod 12) =
1 + 10 (mod 12) = 11
(j) 74
93 (mod 13) =
9
2 (mod 13) = 18 (mod 13) = 5
(k) 33
266 (mod 26) =
7
6 (mod 26) = 42 (mod 26) = 16
2. Complete the following table by either converting the given binary number to decimal
form or vice versa.
Binary
Decimal
(a)
0101
5
(b) 100111
39
(c)
1111
15
(d)
10100
20
(e)
1010101
85
(f)
10010110
150
(g)
101101
45
(h)
111011
59
3. If my birthday was on Monday, January 5, 2015, what day of the week will my birthday
be on this year (2016)?
365 (mod 7) = 350 (mod 7) + 15 (mod 7) = 0 + 1 (mod 7) = 1
My birthday would have been on Tuesday, January 5 , 2016.
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