Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 4
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Common Bases
Modular artihmetic are used in the real world on a daily basis. As we saw in the introduction
of this lesson, base 12 is a common one used in analog clocks. Here are some other commonly
used bases:
Base Application
Example
A number
is even if
(mod 2) = 0, and odd
Even/odd numbers
otherwise.
2
We also use base 2 when using converting from
Binary codes
binary to decimal form, as we will see later.
If any given year
is either [ (mod 400) = 0]
Years between 2 consecutive
4
or [ (mod 4) = 0 and
(mod 100) = 0] then
leap years (in general)
it is a leap year, otherwise it isn’t.
If today is Sunday, then in 16 days it will be
7
Days in a week
a Tuesday (since 16 (mod 7) = 2 ).
We use base 10 when converting between met-
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Metric measurements
ric measurments, such as metres to millime-
tres.
If it’s 7 pm now, it will be 2 am in 7 hours
12
Hours on an analog clock
(since (7 + 7) (mod 12) = 14 (mod 12) = 2).
If its 2 pm now, in 54 hours it will be 8 am
24
Hours in a day
(since (54 + 2) (mod 24) = 8).
28, 29,
If today is the 4 of April, then it will be the
Days in a month
30, 31
8 of May in 34 days.
If today is the 6 week of the year, then it will
52
Weeks in a year
be the 16 week of next year in 62 weeks.
Seconds in a minute and minutes
155 seconds is equivalent to 2 minutes and 35
60
in an hour
seconds.
In 344 years, it will be the 60
year of that
100
Years in a century
century, since (344 + 2016) (mod 100) = 60.
Rotating 420° is equivalent to rotating 60°
360
Degrees in a full circle
since 420 (mod 360) = 60.
If today is the 65 day of the year, then in 750
365
Days in a year
days, it will be 85 day of that year.
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