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Time - Calendar and Date

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Structure of a Year: A year is composed of 1212 months, starting with January and ending with December. Visually, a calendar displays these months in a grid format with 77 columns, where each column represents a day of the week: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday.

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Days in Each Month: Months have varying lengths. January, March, May, July, August, October, and December have 3131 days. April, June, September, and November have 3030 days. February is unique, having either 2828 or 2929 days. You can visualize this using the 'Knuckle Rule', where the raised knuckles represent 3131-day months and the depressions between knuckles represent 3030-day months (or February).

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Ordinary Year vs. Leap Year: An ordinary year has 365365 days. A leap year occurs every 44 years and has 366366 days. The extra day is added to February, making it 2929 days long. Visually, a leap year can be identified on a timeline as every fourth year (e.g., 2016,2020,20242016, 2020, 2024).

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Leap Year Identification: To determine if a year is a leap year, check if the last two digits of the year are divisible by 44. For century years (years ending in 0000 like 19001900 or 20002000), the year must be divisible by 400400 to be a leap year.

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The Week Cycle: There are exactly 77 days in one week. Because 365365 divided by 77 is 5252 with a remainder of 11, an ordinary year consists of 5252 weeks and 11 extra day. A leap year consists of 5252 weeks and 22 extra days.

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Date Formatting: Dates are written in the format Day/Month/Year (DD/MM/YYYYDD/MM/YYYY). For example, 05/10/202305/10/2023 represents the 5th5^{th} day of October in the year 20232023. This helps in organizing chronological events on a timeline.

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Calculating Number of Days: To find the duration between two dates within the same month, we subtract the starting date from the ending date. If both the start and end dates are included in the count, we use the logic: Total Days=(End Date−Start Date)+1\text{Total Days} = (\text{End Date} - \text{Start Date}) + 1.

📐Formulae

1 week=7 days1 \text{ week} = 7 \text{ days}

1 ordinary year=365 days1 \text{ ordinary year} = 365 \text{ days}

1 leap year=366 days1 \text{ leap year} = 366 \text{ days}

1 ordinary year=52 weeks+1 day1 \text{ ordinary year} = 52 \text{ weeks} + 1 \text{ day}

1 leap year=52 weeks+2 days1 \text{ leap year} = 52 \text{ weeks} + 2 \text{ days}

Total Days=(Number of weeks×7)+Remaining days\text{Total Days} = (\text{Number of weeks} \times 7) + \text{Remaining days}

💡Examples

Problem 1:

Convert 88 weeks and 55 days into total days.

Solution:

Step 1: We know that 1 week=7 days1 \text{ week} = 7 \text{ days}. Step 2: Multiply the number of weeks by 77: 8×7=56 days8 \times 7 = 56 \text{ days}. Step 3: Add the remaining days to the result: 56+5=61 days56 + 5 = 61 \text{ days}. Final Answer: 61 days61 \text{ days}.

Explanation:

To convert weeks to days, we use the conversion factor of 77 and then add any additional days provided in the problem.

Problem 2:

How many days are there from 12th12^{th} April to 28th28^{th} April, including both days?

Solution:

Step 1: Identify the start date: 1212. Step 2: Identify the end date: 2828. Step 3: Use the formula for inclusive days: Total Days=(End Date−Start Date)+1\text{Total Days} = (\text{End Date} - \text{Start Date}) + 1. Step 4: Calculate: (28−12)+1=16+1=17 days(28 - 12) + 1 = 16 + 1 = 17 \text{ days}. Final Answer: 17 days17 \text{ days}.

Explanation:

When both the start and end dates are included, simply subtracting the dates leaves out one day, so we must add 11 back to get the correct count.