Sets in Mathematics are the collection of definite objects that can form a group. The collection of numbers, days of the week, types of vehicles,...

Sets

April 11, 2024A **calendar **is an essential tool in our day-to-day life. It helps us keep track of the days, weeks, months, and years. Thus it helps us organise ourselves. With the help of the Calendar, you can keep track of your exams, some important events, festivals etc. A year has \(12\) months which starts with January and ends with December.

In an ordinary year, we have \(365\) days, and we have the leap year every four years, and it has \(366\) days in it. In this article, we will provide detailed information on the Calendar. Scroll down to learn more!

A calendar is a chart of pages representing the days, weeks, and months of a specific year. As you know, the ordinary year consists of (365) days, or a leap year which consists of (366) days, is divided into (12) months. You can see the names of the (12) months in the given table:

Now, there are \(7\) days organised in a week, and you have \(10080\) minutes in a week. And there are \(168\) hours in a week. You can see the names of the week in the below-given table:

Generally, we all use the calendar to keep the record of essential events like festivals, anniversaries, birthdays etc., in the form of the dates. You can see the format of the date that is shown below:

Here, DD represents the days of the month, and that can be \(01\) to \(31\) in the form of two digits.

Now, MM represents the months of the year, and that can be from \(1\) to \(12.\)

The letters YY represent the last two digits of the year like if it is \(2021,\) you will write \(21.\)

When you read a calendar, you will know about the current year, current month, and current day. You can keep yourselves aware of the upcoming events and be prepared for them on their respective dates. Thus, you can keep track of the days, weeks, months, and a year.

When you want to know the day on which Republic day is in \(2021,\) you can simply check the calendar.

You can open the calendar for the year \(2021.\)

Then you open the page of January month.

Now, mark the date of January \(26.\)

Here, in the below-given diagram, you can see that Republic day falls on Tuesday.

A year has \(12\) months. It starts with January and ends with December. It is essential to understand the number of days you have in a month. There are months with \(31\) days, a few months have \(30\) days, and even with \(28/29\) days. Look at the table that is given below:

Usually, you have \(365\) days in a normal year, as the earth rotates about \(365.242375\) times, but you have to count only \(365\) times. Where you have \(366\) days in the leap year, which occurs every fourth year, and you add an extra day, i.e., the \({29^{{\rm{th}}}}\) day of February, which makes up the unseen \(0.25\) days for these four years. So, every fourth year, the month of February has \(29\) days, and that specific year is known as a leap year.

Leap year is the year in which an extra day is added, referred to as the leap day, i.e., February \(29\) is added to the smallest month, which is February. To keep our calendar in alignment with the earth’s revolutions around the Sun, leap days are needed.

**How do we know which year is a leap year?**

Divide the year by \(4.\) If it is fully divisible by \(4,\)it is a leap year.

Example: \(2020\) is divisible by \(4.\) Thus it is a leap year with a February of \(29\) days.

Century years like \(300,\,700,\,1900,\,2000\) and many like these need to be divided by \(400\) to check whether they are leap years or not. For example, a century year like \(2000\) is divisible by \(400,\) so it is a leap year. However, a Century year like \(1900\) is not divisible by \(400.\) Thus it is not a leap year, even though it is divisible by \(4.\)

You can see few points that are given below related to the topic calendar:

\(100\) years \( = 76\) normal years \( + 24\) leap years

\( = \left( {76 \times 1 + 24 \times 2} \right)\) odd days \( = 124\) odd days

\( = (17\) weeks \( + \) days \() = 5\) odd days.

So, \(100\) years gives you \(5\) odd days as calculated above.

\(200\) years gives you \(5 \times 2 = 10 – 7\) (one week) \(3\) odd days.

\(300\) years gives you \(5 \times 3 = 15 – 14\) (two weeks) \(1\) odd day.

\(400\) years gives you \(\left\{ {5 \times 4 + 1\left( {{\rm{leap}}\,{\rm{century}}} \right) – 21} \right\}\) (three weeks) \(0\) odd days.

January month gives you \(31 – 28 = 3\) odd days.

February month gives you \(28 – 28 = 0\) odd days in a normal year, and \(1\) odd day in the leap year etc., you can calculate for all the months in the same way.

We have provided the basic structure of a calendar below:

**Ordinary year:** The year which consists of \(365\) days is known as an ordinary year.

Example: The years \(1879,\,2009,\,2019,\) etc.

**Leap year: **The year which consists of \(366\) days is known as a leap year.

Example: The years \(2012,\,2016,\,2020\) etc.

When the number \(365\) is divided by the number \(7\) you get the quotient of \(52\) and the remainder of \(1\) which means that a normal year has \(52\) weeks and one day extra, and this extra day is known as an odd day all through the topics of the calendar.

When the number \(366\) is divided by the number \(7\) you get the quotient of \(52\) and the remainder of \(2,\) and this means that the leap year has \(52\) weeks and extra two days. These extra two days are also referred to as odd days.

** Q.1. Conversion of \(10\) weeks into months.** In \(10\) weeks total number of the day, we have \(10 \times 7 = 70\) days

Ans:

We know that \(1\) week \( = 7\) days.

Here, \(70\) days \( = 30 + 30 + 10\)

So, you can say that \(10\) weeks is similar to \(2\) months and \(10\) days.

\(\therefore 10\) weeks \( = 2\) months and \(10\) days.

** Q.2. Write the names of the months that have \(30\) days and add and write the total number of days.** We know that the months that have \(30\) days in them are April, June, September, and November.

Ans:

Now, we know all the given months have \(30\) days, so that we will add the number \(30\) for four times, \(30 + 30 + 30 + 30 = 120\) days.

So, the total number of days of April, June, September, and November is \(120\) days.

Hence, the required answer is given above.

** Q.3. Add and write the total number of days the given months have: March, May, June, August, and November.** We know that March has \(31\) days; May has \(31\) days; June has \(30\) days; August has \(31\) days; November has \(30\) days.

Ans:

Now, add the number of days \(31 + 31 + 30 + 31 + 30 = 153\) days.

Thus, the given five months have \(153\) days.

Hence, the required answer is given above.

*Q.4. Write the name of the month which comes in between July and September.*** Ans:** We are given to identify and write the name of the month that comes in between July and September.

Recall the names of the twelve months:

They are January, February, March, April, May, June, July, August, September, October, November, and December.

So, you can see the month that comes in between July and September is August.

Hence, the required answer is August.

*Q.5. Write the name of the day which comes in between Sunday and Tuesday.*** Ans:** We are given to identify and write the name of the day that comes in between Sunday and Tuesday.

Recall the names of the seven days:

They are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.

So, you can see the day that comes in between Sunday and Tuesday is Monday.

Hence, the required answer is Monday.

In the given article, we have discussed the term calendar, reading the calendar, days in each month, followed by the leap year calendar. While reading a calendar you can learn how to learn about the current year, month, and days. Reading the calendar will help us be aware of the upcoming events and to prepare for them effectively. The ordinary year is defined as the year which involves 365 days. The examples for ordinary years are 2009, 2019, etc. The leap year is defined as the year which involves 366 days. The examples for leap year are 2012, 2016, etc.

**Related Topics to Calendar**

1. Time 2. Months in a Calendar |

** Q.1. How do we know whether a year is a leap year?** Divide the year by the number \(4,\) and see if it is fully divisible by \(4,\) then it is a leap year.

Ans:

Example: \(2020\) is divisible by \(4.\) Thus it is a leap year, with February month having \(29\) days.

** Q.2. What are calendar tricks?**The calendar tricks are given below:

Ans:

So, \(100\) years gives you \(5\) odd days as calculated above.

\(200\) years gives you \(5 \times 2 = 10 – 7\) (one week) \(3\) odd days.

\(300\) years gives you \(5 \times 3 = 15 – 14\) (two weeks) \(1\) odd day.

\(400\) years gives you \(\left\{ {5 \times 4 + 1\left( {{\rm{leap}}\,{\rm{century}}} \right) – 21} \right\}\) (three weeks) \(0\) odd days.

January month gives you \(31 – 28 = 3\) odd days.

February month gives you \(28 – 28 = 0\) odd days in a normal year, and \(1\) odd day in the leap year etc., you can calculate for all the months in the same way.

** Q.3. What is the formula of the calendar? **The formula of the calendar is given below:

Ans:

\(1\) ordinary year \( = 365\) days \( = 52\) weeks \( + 1\) day.

\(\therefore 1\) ordinary year has \(1\) odd day.

\(1\) leap year \( = 366\) days \( = 52\) weeks \( + 2\) days

\(\therefore 1\) leap year has \(2\) odd days.

** Q.4. What is the extra day added in a calendar every four years called?**When the number \(365\) is divided by the number \(7\) you get the quotient of \(52\) and the remainder of \(1\) which means that a normal year has \(52\) weeks and one day extra, and this extra day is known as an odd day all through the topics of the calendar.

Ans:

When the number \(366\) is divided by the number \(7\) you get the quotient of \(52\) and the remainder of \(2,\) and this means that the leap year has \(52\) weeks and extra two days. These extra two days are also referred to as odd days.

** Q.5. How to find a day when the date is given in the calendar?** When you want to know the day when the date is given on the calendar, understand this by looking at the following example:

Ans:

You can open the calendar for the year \(2021.\)

Then you open the page of August month.

Now, mark the date of August \({15^{{\rm{th}}}}.\)

Here, in the below-given diagram, you can see that Independence day falls on Sunday.

*We hope this detailed article on calendars helped you in your studies. If you have any doubts or queries, you can reach out to us through the comment section and we will help you at the earliest. *