Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 12
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1313. Look back at the table titled “Common Bases”
(a) Was the year 1900 a leap year?
We will calculate 1900 modulo 4, 100 and 400 to test if it was a leap year or not.
1900 (mod 4) = 0
1900 (mod 100) = 0
1900 (mod 400) = 300
No, 1900 wasn’t a leap year, since 1900 (mod 4) = 0 and 1900 (mod 100) = 0
but 1900 (mod 400) = 0
(b) Was the year 2000 a leap year?
Similarily, we will calculate 2000 modulo 4, 100 and 400 to test if it was a leap
year or not.
2000 (mod 4) = 0
2000 (mod 100) = 0
2000 (mod 400) = 0
Yes, 2000 was a leap year.
(c) Is the year 2100 going to be a leap year?
We will calculate 2100 modulo 4, 100 and 400 to test if it will be a leap year or
not.
2100 (mod 4) = 0
2100 (mod 100) = 0
2100 (mod 400) = 100
No, 2100 will not be a leap year.
(d) Is the year 2200 going to be a leap year?
We will calculate 2200 modulo 4, 100 and 400 to test if it will be a leap year or
not.
2200 (mod 4) = 0
2200 (mod 100) = 0
2200 (mod 400) = 200
No, 2200 will not be a leap year.
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