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Arithmetic (Beginner) · Quick Reference
Time & Calendar Cheat Sheet
In one line: calendar problems use patterns in days, weeks, and years to figure out things like what day a date falls on, or how leap years work.
Key Ideas
1Days in a Week. There are 7 days in a week, so days repeat in a cycle of 7.
2Odd Days. The number of days left over after dividing total days by 7 — used to find what day of the week a date falls on.
3Leap Year Rule. A year is a leap year if divisible by 4, except century years (ending in 00), which must be divisible by 400.
4Days in Each Month. 30 days: April, June, September, November. 31 days: the rest, except February (28, or 29 in a leap year).
5Ordinary vs. Leap Year Odd Days. An ordinary year has 1 odd day (365 = 52 weeks + 1 day). A leap year has 2 odd days (366 = 52 weeks + 2 days).
Worked Examples
Is the year 2024 a leap year?
Yes, 2024 is a leap year
Is the year 1900 a leap year?
No, 1900 is not a leap year
If January 1 is a Monday, what day is January 15?
Monday
Formulas
Odd days = Total days mod 7
Practice Yourself
Is 2028 a leap year?
Yes (divisible by 4, not a century year)
Is 2000 a leap year?
Yes (divisible by 400)
How many odd days does an ordinary year have?
1