Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016


Faculty of Mathematics
Centre for Education in
Waterloo, Ontario N2L 3G1
Mathematics and Computing
Grade 7/8 Math Circles
February 9-10, 2016
Modular Arithmetic
Introduction: The 12-hour Clock
Question: If it’s 7 pm now, what time will it be in 7 hours?
2 am
How about in 30 hours?
1 am after tomorrow
Now, this is a simple example that we’re all familiar with, but how did we actually calculate
this? Can you simplify this into 2 or 3 simple steps?
Add 7 (time it is now) to 7 or 30 (number we’re asked to add).
Keep subtracting 12 from this sum until you get a number less than 12.
Review of Divisibility
Definition: An integer
is divisible by an integer
is an integer (ie. there is no
remainder when x is divided by n). We write
, which is read “ is divisible by ”.
Can you think of another way to ask “Is x divisible by n?”
Exercise 1
(a) Is 15 divisible by 3?
(b) Is 75 divisible by 2?
Note: this is another way of asking if 75 is even
(c) Is 50 divisible by 15?
(d) is 150 divisible by 3?


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